The distribution of the projected centre-to-centre separations of all LMC cluster pairs is displayed in Fig. 7 (solid line). Two peaks around 6 pc and approximately 15 pc are apparent. The peak around 6 pc as well as the subsequent decline around 9 pc are independent of binning. The median separation of the sample is $11.9\pm5.2$ pc, the mode (the most probable value) is 6.3 pc. The number of cluster pairs with a separation of 10 pc and larger increases, but seems to level off or even decrease again at separations of 18 pc and larger.

To constrain our presumption we performed a KMM ("Kaye's mixture model'', see Henriksen et al. 2000) test. Basically, mixture modelling is used to detect clusterings in datasets and to assess their statistical significance. The KMM fits a user-specified number of Gaussians to a dataset. The algorithm iteratively determines the best positions of the Gaussians and assigns to each data point a maximum likelyhood estimate of being a member of the group. It also compares the fit with the null-assumption, that is a single Gaussian fit to the dataset, and evaluates the improvement over the null-assumption using a "likelyhood ratio test statistic''. The algorithm is described in detail in Ashman et al. (1994). The user has to provide as an input the number of data points, an initial guess for the number of groups, their positions, and sizes. A great advantage of KMM is that it works on the data themselves and is not applied to the histogram, thus it is completely independent of binning and not affected by any subjective visual impression.

For our first guess, we assumed two distributions with positions (i.e., the mean of the Gaussians) at 6 and 15 pc, 4 pc as the standard deviation of the Gaussians, and a mixing proportion of 0.4 and 0.6 for the two groups. The number of data points assigned to each group by KMM is 325 and 440 with estimated correct allocation rates of 0.914 and 0.944 for the two groups. The estimated overall correct allocation rate is 0.931. The estimated means of the two groups are 6.644 and 15.442 (close to our assumed positions). The hypothesis that the distribution can be fitted by a single Gaussian is rejected with more than 99% confidence.

It might be possible that the underlying distribution is best described with three Gaussians. Our input guess for this case was means at 6, 13, and 18 pc, a common standard deviation of 3, and mixing proportions of 0.4, 0.3, and 0.3. The KMM assigns 239, 239, 287 members to each group, with allocation rates of 0.936, 0.845, and 0.925 and an overall correct allocation rate of 0.903. The KMM estimated positions are at 5.368, 11.599, and 17.043. Again, the null-assumption is rejected with more than 99% confidence. Compared to our first, two-Gaussian guess, the KMM estimate for the overall correct allocation rate is smaller. We conclude that the distribution is better described with a two-Gaussian distribution.

Bhatia & Hatzidimitriou (1988) investigated the separations of their 69 proposed binary clusters and found a bimodal distribution with peaks around 5 and 15 pc, similar to our findings if a two-Gaussian distribution is assumed. Bhatia et al. (1991) further suggested a more uniform distribution for cluster pairs in which both clusters have diameters larger than 7 pc. However, a uniform distribution for large clusters can be explained in the following way: the larger the components of a cluster pair, the larger the probability that both clusters are overlapping and may not be detected as a cluster pair but as only one single large cluster. It is likely that the catalogue is not complete concerning cluster pairs in which both clusters are large but have a small separation. Based on our catalogue of binary and multiple cluster candidates, we reinvestigated the distribution of separations for cluster pairs in which both components have diameters either larger or smaller than 7 pc. The dashed line in Fig. 7 denotes pairs consisting of large clusters while the dotted line stands for pairs with small components. Indeed, the bimodal distribution is most apparent for small components and seems to be peaked around approximately 5 and 15 pc, in agreement with the findings of Bhatia et al. (1991). For pairs consisting of large clusters, a bimodal distribution is not as apparent, but cannot be neglected either. We cannot confirm a uniform distribution of separations for pairs with large clusters.

A general increase in the number of pairs as a function of separation is obvious from Fig. 7. This increase can be expected because cluster pairs with larger separations between the components can more easily be detected than close couples of clusters which might overlap and thus "merge'' into one single cluster. Besides, the probability of finding another cluster increases with increasing separation (and thus increasing area).

On the other hand, for a given separation between cluster pairs, we expect to find an increase in the number of binary cluster candidates towards smaller separations since the "projected'' separations are smaller than the real one. This might explain the first peak around 6 pc in the distribution of separations. The decrease towards separations smaller than 6 pc can be expected since clusters with small separations likely overlap and thus are difficult to detect. Consequently, the dip around 9-10 pc might be interpreted as a balance between the effects that lead to an increase in the number of cluster pairs towards either smaller or larger separations.

6.2 Size distribution

The size distribution of clusters that are part of cluster pairs or groups is displayed in the upper diagram of Fig. 8. Most components of the cluster pairs are small. They have diameters between $0.2 \hbox{$^\prime$ }$ ( $\approx$ 3 pc) and $1\farcm5$ ( $\approx$ 22 pc) with a clear peak at $0\farcm45$ ( $\approx$ 6.6 pc). The median diameter of the sample is $0\farcm57 \pm 0\farcm26$ ( ${\approx} 8.5 \pm 3.8$ pc), the mode is at $0\farcm48$ ( $\approx$ 7 pc). Only a few clusters have diameters larger than $1\farcm8$ ( $\approx$ 26 pc). However, in spite of our selection criterion of a separation of 20 pc, we still find three clusters with diameters larger than 40 pc ( $2\farcm7$ ). This means that their companion cluster is embedded within their circumference. These clusters are NGC 1850 (or BRHT 5 a) with its companions NGC 1850 A and BRHT 5 b (or H88-159), and NGC 2214 which appears in the BSDO catalogue as two entries, namely NGC 2214 w and NGC 2214 e.

The lower diagram in Fig. 8 shows the diameter distribution for all clusters found in the BSDO catalogue. Again, most clusters are rather small with a peak at $0\farcm45$ or $\approx$ 6.6 pc. The median diameter of the entire cluster sample is $0\farcm62 \pm 0\farcm41$ ( ${\approx} 9 \pm 6$ pc) and the mode is $0\farcm55$ or $\approx$ 8 pc.

The normalized ratio of the diameters of clusters that form a pair are plotted in Fig. 9. The median ratio of the sample is $0.73 \pm 0.2$ . The number of cluster pairs increases towards a size ratio of 0.5, but drops at a ratio larger than 0.5 and lower or equal than 0.55, and then increases again towards a ratio of 1. The number of pairs increases with larger ratios, which might indicate that binary clusters tend to form with components of similar sizes.

The dotted line in Fig. 9 represents the size ratio of cluster pairs if all diameters are mixed and then randomly assigned to the pair members. To get reliable statistics we repeated this procedure 100 times. The number of pairs increases with increasing ratio, but seems to decrease again at ratios larger than 0.75, which confirms the impression that "true'' binary clusters tend to form with components of similar sizes. Again, there is a peak at 0.5 and a following dip at ratios slightly larger than 0.5, though not as prominent as in the distribution of found ratios (solid line). However, a uniform distribution is not expected for statistical reasons: the diameters of the clusters in the BSDO catalogue are given in arc minutes in steps of $0\farcm05$ , i.e., the smallest diameter is $0\farcm25$ , the next one $0\farcm3$ and so on. Since we consider mean diameters, we obtain discrete values with an increment of $0\farcm025$ . This means that some ratios are more probable than other ones, namely the unit fractions, which includes a ratio of 0.5 = 1/2, while other ratios might result only few times in the distribution. For example, a ratio of 34/35 can only result from three combinations of diameters in the given distribution of diameters, namely if both components of the pair have diameters of $0\farcm85$ and $0\farcm875$ , or $1\farcm7$ and $1\farcm75$ , or $2\farcm55$ and $2\farcm625$ . In the real ratio distribution it occurs only once for 0.85/0.875. This explains the peak at 0.5 as one of the very likely ratios in the distribution. However, in general the distribution of the found ratios and the distribution of the ratios for scrambled diameters agree well with each other, though there might be a tendency of the real binary cluster candidates to form more pairs with components of similar sizes.

6.3 Spatial distribution of the cluster pairs and groups

Figure 10 represents the location of all cluster pairs found in the LMC. The distribution of all pairs reflects the dense bar region and the region around the bar ( $E_{\rm bar}$ ). The pair density drops considerably in the outer LMC region. Altogether, the distribution of cluster pairs is very similar to the distribution of clusters in general and there are no regions of increased pair density that do not correlate with the distribution of clusters.

Bhatia et al. (1991) suggested that pairs with small clusters are predominantly found outside the central region of the LMC. However, they caution that this effect might also be due to the increasing incompleteness for small clusters in their data towards the crowded inner LMC. We reinvestigated the distribution for cluster pairs in which both components are either larger (diamonds in Fig. 10) or smaller (crosses in Fig. 10) than 7 pc. Most cluster pairs have large components, in total 336 pairs. 136 pairs have only small clusters, and the remaining 293 couples have a small as well as a large component. It seems that in the outer LMC comparably more pairs with large clusters can be found than pairs with small components. The ratio of pairs with only large components and pairs with only small ones is 336/136=2.46. If only pairs in the inner parts of the LMC (marked with a circle in Fig. 10) are considered, the ratio is 200/75=2.67, for the outer region it is 136/61=2.23. This means that in the outer as well as in the inner LMC, more pairs with only large components than pairs with only small clusters can be found, however, in the outer LMC we find proportionally more pairs with only small clusters compared to the inner LMC. However, in total numbers most of the pairs with only small components are found in the inner parts of the LMC, opposite to the suggestion of Bhatia et al. (1991).

In general, the distributions seem to follow the distribution of cluster pairs and we do not see regions that are primarily populated with pairs of a specific "type'' that differ from the general distribution of clusters. We cannot confirm the accumulation of pairs with only small clusters in the outer LMC region as suggested by Bhatia et al. (1991). Their finding is likely an effect of the incompleteness of their data (they considered 69 binary cluster candidates whereas our sample includes 765 cluster pairs).

6.4 Ages of the binary and multiple cluster candidates

We have searched for ages of the binary and multiple cluster candidates in the literature. Age information is available only for a fraction of all the clusters in our catalogue. It turned out that out of a total of 473 groups only 186 groups have age information available, and the information is complete for all group components only for a fraction of these groups. In total, we found ages for only 306 clusters, which are $\approx$ 27% of the 1126 clusters that form pairs and groups. The most fruitful sources were the publications of Bica et al. (1996), who estimated ages from integrated UV photometry, and of the OGLE group, who fitted isochrones to CMDs (Pietrzynski & Udalski 2000a). All results are summarized in Table 6 where we also give the corresponding references. This catalogue contains all binary and multiple cluster candidates found in the entire LMC, based on the BSDO catalogue (see Sect. 4 where we noted the different number of groups found in the entire LMC and the sum of the groups found in all regions separately).

In Fig. 11 we plotted a histogram of the age distribution for our binary and multiple cluster candidates. If more than one age was determined for a cluster we averaged the values. However, if the ages found by various authors differ considerably we adopt the value found in the most recent studies since the methods of age determinations have improved in the recent years, e.g., ages derived from isochrone fitting to CMDs based on CCD photometry are generally considered the most reliable and accurate age determinations.

An example is NGC 1775 for which Bica et al. (1996) estimated an age of 70-200 Myr while Kontizas et al. (1993) stated that the stars in NGC 1775 are too faint for their detection limit and thus suggested an age larger than 600 Myr. Since Bica et al. (1996) did not report detection problems for this object, we adopt a mean age of 135 Myr for this cluster to be plotted in Fig. 11.

An example for which ages derived from isochrone fitting is available is SL 353 & SL 349: CCD based CMDs were investigated by Dieball et al. (2000) and by Vallenari et al. (1998) and both studies agree with ages of 550 Myr for both clusters. Bica et al. (1996) derived an age of 1.4 Gyr from integrated colours. However, Geisler et al. (1997) pointed out that a few bright stars can influence the age determination based on integrated photometry, making the result dependent on the chosen aperture. Pietrzynski & Udalski (2000a) fitted isochrones to CMDs and suggested an age of 1 Gyr for SL 353 and 450 Myr for SL 349. These authors used a distance modulus of 18.24 mag and fitted isochrones based on the stellar models of the Padua group (Bertelli et al. 1994), whereas we use a modulus of 18.5 mag and isochrones based on the Geneva models (Schaerer et al. 1993). However, Vallenari et al. (1998) also used the Padua isochrones and their results agree with ours. The smaller distance modulus of 18.24 mag would lead to larger ages, this cannot explain the smaller age that Pietrzynski & Udalski (2000a) found for SL 349 and the age difference suggested for the cluster pair. In Fig. 12 we compare their isochrone fit with ours. It seems that their suggested age for SL 349 is too young while the age for SL 353 seems to be too old to give a good fit. Isochrones representing the ages we adopted for this cluster pair are also plotted (see Dieball et al. 2000 for the details).

In cases where several consistent age determinations are available, but one value differs from the others, we omit the "outlier'' and average the other results. This is the case, e.g., for SL 229. For this cluster Fujimoto & Kumai (1997) derived an age of 460 Myr, Bica et al. (1996) suggested an age of 200-400 Myr, and Pietrzynski & Udalski (2000a) 220 Myr, however, Kontizas et al. (1993) proposed 6-80 Myr. We adopt a mean of 330 Myr. For the companion cluster SL 230 the age determinations agree better: 74 Myr (Fujimoto & Kumai 1997), 20 Myr (Bica et al. 1996), 43 Myr (Kontizas et al. 1993), and 140 Myr (Pietrzynski & Udalski 2000a). We adopt 70 Myr, which agrees with Fujimoto & Kumai (1997) and Kontizas et al. (1993), but is a higher value than suggested by Bica et al. (1996) and lower than suggested by Pietrzynski & Udalski (2000a).

In this way different ages for the same cluster are averaged to a mean age, however, the main information, which is if the clusters of a group have ages similar enough to agree with a common formation or not, is obtained in all cases.

In some cases no ages could be found for the specific clusters of a group, but an age determination of the surroundings, e.g., the association the clusters are embedded in, is available and is adopted for the plot in Fig. 11. For example, we assume an age of 5 Myr for BSDL 1437 & HD 269443, which are both embedded in LMC N 44 D for which Bica et al. (1996) derived a mean age of 5 Myr. In such a case a congruous remark is made in Table 6.

For only 96 groups age information is available for more than one cluster, which allows a closer look at the age structure of the specific group, though ages are rarely found for "all'' clusters of a group.

If clusters have formed from the same GMC, they should be coeval or have age differences that are small enough to agree with a common formation, i.e., the age difference must be smaller than the maximum life time of a GMC. Fujimoto & Kumai (1997) suggested that the life time of a protocluster gas cloud is of the order of a few 10 Myr. However, more recently Fukui et al. (1999) and Yamaguchi et al. (2001) suggested that the life time of a GMC is of the order of only a few Myrs:

Fukui et al. (1999) conducted a CO survey of the LMC, catalogued the CO clouds, and correlated their positions with all clusters listed in the Bica et al. (1996) catalogue, which contains also age estimates for the clusters. Fukui et al. (1999) found a significant correlation of the positions of the youngest clusters (SWB 0, age $\leq$ 10 Myr) with nearby CO clouds. In contrast, the location of older clusters (SWB II-SWB VII) with respect to nearby CO clouds was found to be consistent with a random distribution, i.e., they can easily be explained as line-of-sight chance superpositions. The authors suggested that star clusters are formed rapidly in a few Myr after cloud formation and that the cloud dissipates quickly on a time scale of 6 Myr. More recently, Yamaguchi et al. (2001) suggested that the GMCs actively form star clusters for about 4 Myr, and that they are completely dissipated due to the winds and supernova explosions of massive stars within the following 6 Myr (Yamaguchi et al. 2001, their Table 5). Fukui et al. (1999) found that approximately 30% of the young clusters with ages < 10 Myr are located within 130 pc from the surviving CO clouds. This implies that the time scale for the joint formation of a cluster pair that fulfill our criterion of 20 pc must be on average less than 10 Myr. This results in a rather stringent age criterion for true binary clusters.

On the other hand, we need to take into account that for clusters of an age of $\approx$ 100 Myr and older the age resolution is worse than 10 Myr and continues to decrease. Hence it seems to be justified to consider two components of a potential binary cluster coeval when their ages agree within the uncertainties of their age determination.

In 57 groups at least two clusters appear to be either coeval or have ages similar enough to agree with a common formation in the same GMC, i.e., the age differences are smaller than 10 Myr. To be able to plot the group ages (see Fig. 11, lower diagram) we have averaged the ages of the group members and assigned a mean age to the corresponding group. For some of the older clusters, the age difference inside the group can be larger than 10 Myr, but still within the errors the group components agree with the same age (see text above). This is the case, e.g., for group no. 206 where Pietrzynski & Udalski (2000a) derived an age of 500 Myr for KMK 88-49. For NGC 1938, Pietrzynski & Udalski (2000a) found an age of 355 Myr, Fujimoto & Kumai (1997) estimated an age of 550 Myr, Bica et al. (1996) suggested 200-400 Myr, Kontizas et al. (1993) suggested an age >600 Myr. We adopt a mean of $450\pm140$ Myr for NGC 1938. Within the errors, both clusters, NGC 1938 and KMK 88-49, agree well with a common formation from the same GMC. For the third component of this group, NGC 1939, all age estimates lead to higher ages of 7 Gyr (Fujimoto & Kumai 1997), 5-16 Gyr (Bica et al. 1996), >600 Myr (Kontizas et al. 1993), and 1 Gyr (Pietrzynski & Udalski 2000a). We adopt a mean of 5 Gyr. It is clear that NGC 1939 is considerably older than the other two clusters of this group and cannot have formed together with the other two components. In general, the error of the age determination is the larger the older the cluster is. The groups that for this reason show somewhat higher internal age differences than our selection criterion of 10 Myr are nos. 90, 94, 124, 135, 180, 184, 206, 211, 243, 428, and 456. In the remaining 39 groups the age difference(s) found well exceed 10 Myr (also when the errors in the age determination are considered) which is more than the maximum life time of protocluster gas clouds (Fukui et al. 1999; Yamaguchi et al. 2001). As a result, these clusters cannot have a common origin.

In Fig. 11, upper diagram, the ages of all clusters with available age information are plotted. As can be seen, the clusters are predominantly young (a few 10 Myr to 100 Myr) or very young (a few Myr) with significant peaks at 4 Myr, 25 Myr, and 100 Myr. Smaller peaks are at 10 Myr and 400 Myr. Only a few clusters are older than 1 Gyr, and if so, their companion cluster(s) is of a different (younger) age which makes it likely that the specific group appears close on the sky only due to projection effects. An exception is group no. 11 where both clusters have an age of 1.2 Gyr. We agree with Pietrzynski & Udalski (2000b) that most clusters are younger than 300 Myr. The peak at 100 Myr might be explained by a close encounter of both Magellanic Clouds roughly 200 Myr ago that triggered star and cluster formation (Gardiner et al. 1994). However, our age distribution for the group components differs from the one presented by Pietrzynski & Udalski (2000b). The pronounced peaks at 4 and 25 Myr are missing in Pietrzynski & Udalski's (2000b) age distribution, which is due to the fact that these authors investigated only the central part of the LMC whereas we study the whole LMC area. Most of the clusters younger than 30 Myr are located outside the LMC bar, whereas older clusters are concentrated towards the bar region (see e.g. Fig. 13). In addition, the smaller distance modulus of 18.24 mag used by Pietrzynski & Udalski (2000a) also leads to higher ages. The dashed line in Fig. 11 shows the age distribution of the clusters and groups if the OGLE ages (Pietrzynski & Udalski 2000a) are not considered. As can be seen, the OGLE ages are the major contribution to clusters with ages of 100 Myr or older.

In Fig. 13 the location of the old groups (older than 300 Myr, plotted as crosses) and groups with internal age differences which do not agree with a common formation of the group components (indicated as dots) are plotted. As can be seen, most of these groups are located in the dense bar region and thus can easily be explained with chance superpositions.

Group no. 83 comprises a binary cluster candidate, BRHT 3b and KMK 88-4. For both clusters, Pietrzynski & Udalski (2000a) derived an age of 630 Myr. Two more clusters can be found in this cluster group: H 88-107 (710 Myr, Pietrzynski & Udalski 2000a) and NGC 1830. For the latter cluster we adopt a mean age of 275 Myr. H 88-107 is too old to agree with a common formation together with the binary cluster candidate, and NGC 1830 is too young. These two clusters are most probably chance superpositions. Also groups nos. 14, 110, 180, 206, and 258 contain a binary or triple cluster candidate and one ore more components that do not agree with a common formation. These groups are plotted as diamonds in Fig. 13. Nearly all of them are located in the dense bar region.

The upper diagram of Fig. 14 shows the distribution of group ages if all ages for the clusters are scrambled and then randomly assigned to the group members for which the age information was available. In this way, the groups' mean ages change, but also the number of groups which a mean age can be ascribed to varies. We repeated this procedure 100 times to get reliable statistics. On average, $12.9\pm2.7$ groups per run have two or more clusters that are either coeval or have age differences small enough to agree with a common formation so that a mean age could be assigned to the corresponding group.

Table 6: Catalogue of all binary and multiple cluster candidates found in the entire LMC area. Identifiers and remarks, coordinates, object type, maximum and minimum diameter ( $D_{\rm max}$ and $D_{\rm min}$ ) and the position angle (PA) are taken from BSDO. For the acronyms of the objects see BSDO, their Table 1. The acronym used in the OGLE catalogue of star clusters in the LMC (e.g., LMC0012, Pietrzynski & Udalski 2000a) is also given. The $9{\rm th}$ column gives the separations (d) in pc found in the corresponding group, assuming a distance modulus of 18.5 mag. The last column gives the ages available in the literature, the notes follow the table. In some cases, only an age for the association of which the cluster appears to be part is found. If so, a corresponding remark is given in brackets. Only the first 21 groups are listed, the complete table can be found at CDS, Strasbourg
no. identifiers & remarks $\alpha$ $\delta$ type $D_{\rm max}$ $D_{\rm min}$ PA d age

[ $^{\rm h} ~^{\rm m} ~^{\rm s}$ ] [ $^{\circ} ~\hbox{$^\prime$ }~\hbox{$^{\prime\prime}$ }$ ] [ $\hbox{$^\prime$ }$ ] [ $\hbox{$^\prime$ }$ ] [ $^{\circ}$ ] [pc] [Myr]

1 SL23, LW36, HS24, BRHT23b, KMHK50 4 43 38 -69 42 44 CA 1.10 0.95 100 9.1 -

1 SL23A, BRHT23a, KMHK52 4 43 43 -69 43 11 CA 0.85 0.70 60 9.1 -

2 BSDL8 4 43 59 -68 45 22 AC 0.65 0.50 150 9.0 -

2 BSDL9 4 43 59 -68 45 59 AC 0.45 0.35 100 9.0 -

2 LW39, KMHK54 4 43 59 -68 46 43 CA 0.95 0.85 60 19.7 -

2 LW41, KMHK59 4 44 11 -68 44 57 C 0.90 0.90 - 17.0 -

3 BSDL10 4 44 05 -69 52 50 C 0.35 0.30 110 19.9 -

3 SL24, LW38, KMHK55 4 43 50 -69 52 23 C 1.10 1.10 - 19.9 -

4 BRHT59a, KMHK61 (in BSDL7) 4 44 13 -71 22 01 C 0.90 0.65 140 10.3 >600 (x)

4 LW43, BRHT59b, KMHK62 (in BSDL7) 4 44 16 -71 22 41 C 0.90 0.90 - 10.3 >600 (x)

5 BSDL14 4 44 59 -70 18 19 CA 0.50 0.40 40 16.3 -

5 BSDL15 4 44 59 -70 19 26 CA 0.55 0.50 160 16.3 -

6 LW56e, KMHK83e 4 45 54 -72 21 08 C 0.50 0.50 - 2.4 -

6 LW56w, KMHK83w 4 45 52 -72 21 04 C 0.60 0.60 - 2.4 -

7 BSDL25 4 46 24 -72 33 28 AC 0.85 0.75 140 9.1 -

7 SL33, LW59, KMHK91 4 46 25 -72 34 05 C 1.10 1.10 - 9.1 -

8 BSDL55 (in BSDL56) 4 49 25 -69 27 55 AC 0.70 0.55 70 11.6 -

8 HS34 (in BSDL56) 4 49 31 -69 28 31 AC 0.50 0.40 10 11.6 -

9 KMHK136 4 50 12 -68 59 49 AC 1.00 0.85 80 3.0 10-30 (e)

9 SL49 in KMHK136 4 50 10 -68 59 55 C 0.70 0.60 170 3.0 10-30 (e)

10 BSDL104 (in NGC1712) 4 51 10 -69 23 42 CN 0.65 0.55 110 13.9 0-10 (NGC1712) (e), 20 (y)

10 BSDL96 (in NGC1712) 4 51 01 -69 23 10 C 0.90 0.75 70 13.9 0-10 (NGC1712) (e)

11 LW75, SL59w, KMHK152, BRHT24a 4 50 14 -73 38 47 C 1.20 1.10 0 11.4 1200 (s), >600 (x)

11 LW76, SL59e, KMHK157, BRHT24b 4 50 25 -73 38 53 C 1.20 1.10 20 11.4 1200 (s), >600 (x)

12 BSDL100 (in BSDL101) 4 50 58 -70 00 30 AC 0.50 0.35 20 13.4 -

12 BSDL103 (in BSDL101) 4 51 03 -70 00 43 CA 0.50 0.35 60 7.0 -

12 KMHK156 (in SGshell LMC7) 4 51 00 -70 01 24 CA 0.90 0.80 120 13.4 -

13 KMHK164 (in BSDL110) 4 51 23 -69 35 04 C 0.50 0.45 130 16.0 -

13 KMHK166 (in BSDL110) 4 51 32 -69 34 18 AC 0.55 0.55 - 16.0 -

14 BSDL120 (in LMC N79A) 4 51 47 -69 23 14 NC 0.85 0.70 10 7.2 -

14 BSDL124 (in BRHT1a) 4 51 51 -69 24 02 NC 0.50 0.40 110 12.7 0-10 (e), 25 (r)

14 BSDL126 (in LMC N79A) 4 51 53 -69 23 26 NC 0.65 0.50 140 8.2 -

14 IC2111, ESO56EN13, BRHT1b 4 51 51 -69 23 35 NC 0.65 0.55 130 7.2 2-3 (F), 3.7-4.3 (i)

(in LMC N79A)

14 KMHK171 (in BRHT1a) 4 51 53 -69 24 24 NC 0.90 0.90 - 18.7 0-10 (e), 25 (r)

14 LMC-N79B (in NGC1722=BRHT1a) 4 52 00 -69 23 43 NC 0.40 0.35 140 18.1 0-10 (e), 25 (r)

15 BSDL129 4 51 56 -70 23 52 CA 0.40 0.35 70 7.4 -

15 SL66, KMHK180 4 51 55 -70 23 22 C 1.20 1.10 130 7.4 2000 - 5000 (e)

16 H88-11, H80F1-10 4 52 20 -68 59 32 AC 0.50 0.35 30 16.8 -

16 H88-7, H80F1-8 4 52 12 -69 00 26 AC 0.55 0.40 80 16.8 -

17 BSDL155 (in LMC DEM13) 4 53 13 -68 01 48 AC 0.50 0.40 130 19.9 -

17 HDE268680 (in NGC1736) 4 53 03 -68 03 06 NC 0.95 0.80 110 6.8 0-10 (e)

17 LMC-S6 (in NGC1736) 4 53 08 -68 03 05 NC 0.35 0.35 - 6.8 0-10 (e)

18 BSDL157 (in SGshell LMC7) 4 53 00 -69 38 42 AC 0.50 0.45 60 18.7 -

18 KMHK207 (in SGshell LMC7) 4 53 00 -69 37 25 C 0.75 0.75 - 18.7 -

19 BSDL158 4 53 09 -68 38 34 AC 0.50 0.50 - 7.1 -

19 NGC1732, SL77, ESO56SC17, KMHK209 4 53 11 -68 39 01 C 1.10 1.00 50 7.1 30 - 70 (e)

20 KMHK212 (in NGC1731) 4 53 35 -66 55 25 C 0.75 0.60 170 8.6 <4 (NGC1731) (G)

20 SL82, KMHK211 (in NGC1731) 4 53 29 -66 55 28 AC 0.85 0.60 100 8.6 <4 (NGC1731) (G)

21 BSDL162 4 53 24 -67 53 00 AC 0.55 0.55 - 19.1 -

21 HS56, KMHK218 4 53 36 -67 52 20 CA 0.75 0.70 50 19.1 -

**Table 6:** Catalogue of all binary and multiple cluster candidates found in the entire LMC area. Identifiers and remarks, coordinates, object type, maximum and minimum diameter ( $D_{\rm max}$ and $D_{\rm min}$ ) and the position angle (PA) are taken from BSDO. For the acronyms of the objects see BSDO, their Table 1. The acronym used in the OGLE catalogue of star clusters in the LMC (e.g., LMC0012, Pietrzynski & Udalski 2000a) is also given. The $9{\rm th}$ column gives the separations (d) in pc found in the corresponding group, assuming a distance modulus of 18.5 mag. The last column gives the ages available in the literature, the notes follow the table. In some cases, only an age for the association of which the cluster appears to be part is found. If so, a corresponding remark is given in brackets. Only the first 21 groups are listed, the complete table can be found at CDS, Strasbourg
no.	identifiers & remarks	$\alpha$	$\delta$	type	$D_{\rm max}$	$D_{\rm min}$	PA	d	age
		[ $^{\rm h} ~^{\rm m} ~^{\rm s}$ ]	[ $^{\circ} ~\hbox{$^\prime$ }~\hbox{$^{\prime\prime}$ }$ ]		[ $\hbox{$^\prime$ }$ ]	[ $\hbox{$^\prime$ }$ ]	[ $^{\circ}$ ]	[pc]	[Myr]
1	SL23, LW36, HS24, BRHT23b, KMHK50	4 43 38	-69 42 44	CA	1.10	0.95	100	9.1	-
1	SL23A, BRHT23a, KMHK52	4 43 43	-69 43 11	CA	0.85	0.70	60	9.1	-
2	BSDL8	4 43 59	-68 45 22	AC	0.65	0.50	150	9.0	-
2	BSDL9	4 43 59	-68 45 59	AC	0.45	0.35	100	9.0	-
2	LW39, KMHK54	4 43 59	-68 46 43	CA	0.95	0.85	60	19.7	-
2	LW41, KMHK59	4 44 11	-68 44 57	C	0.90	0.90	-	17.0	-
3	BSDL10	4 44 05	-69 52 50	C	0.35	0.30	110	19.9	-
3	SL24, LW38, KMHK55	4 43 50	-69 52 23	C	1.10	1.10	-	19.9	-
4	BRHT59a, KMHK61 (in BSDL7)	4 44 13	-71 22 01	C	0.90	0.65	140	10.3	>600 (x)
4	LW43, BRHT59b, KMHK62 (in BSDL7)	4 44 16	-71 22 41	C	0.90	0.90	-	10.3	>600 (x)
5	BSDL14	4 44 59	-70 18 19	CA	0.50	0.40	40	16.3	-
5	BSDL15	4 44 59	-70 19 26	CA	0.55	0.50	160	16.3	-
6	LW56e, KMHK83e	4 45 54	-72 21 08	C	0.50	0.50	-	2.4	-
6	LW56w, KMHK83w	4 45 52	-72 21 04	C	0.60	0.60	-	2.4	-
7	BSDL25	4 46 24	-72 33 28	AC	0.85	0.75	140	9.1	-
7	SL33, LW59, KMHK91	4 46 25	-72 34 05	C	1.10	1.10	-	9.1	-
8	BSDL55 (in BSDL56)	4 49 25	-69 27 55	AC	0.70	0.55	70	11.6	-
8	HS34 (in BSDL56)	4 49 31	-69 28 31	AC	0.50	0.40	10	11.6	-
9	KMHK136	4 50 12	-68 59 49	AC	1.00	0.85	80	3.0	10-30 (e)
9	SL49 in KMHK136	4 50 10	-68 59 55	C	0.70	0.60	170	3.0	10-30 (e)
10	BSDL104 (in NGC1712)	4 51 10	-69 23 42	CN	0.65	0.55	110	13.9	0-10 (NGC1712) (e), 20 (y)
10	BSDL96 (in NGC1712)	4 51 01	-69 23 10	C	0.90	0.75	70	13.9	0-10 (NGC1712) (e)
11	LW75, SL59w, KMHK152, BRHT24a	4 50 14	-73 38 47	C	1.20	1.10	0	11.4	1200 (s), >600 (x)
11	LW76, SL59e, KMHK157, BRHT24b	4 50 25	-73 38 53	C	1.20	1.10	20	11.4	1200 (s), >600 (x)
12	BSDL100 (in BSDL101)	4 50 58	-70 00 30	AC	0.50	0.35	20	13.4	-
12	BSDL103 (in BSDL101)	4 51 03	-70 00 43	CA	0.50	0.35	60	7.0	-
12	KMHK156 (in SGshell LMC7)	4 51 00	-70 01 24	CA	0.90	0.80	120	13.4	-
13	KMHK164 (in BSDL110)	4 51 23	-69 35 04	C	0.50	0.45	130	16.0	-
13	KMHK166 (in BSDL110)	4 51 32	-69 34 18	AC	0.55	0.55	-	16.0	-
14	BSDL120 (in LMC N79A)	4 51 47	-69 23 14	NC	0.85	0.70	10	7.2	-
14	BSDL124 (in BRHT1a)	4 51 51	-69 24 02	NC	0.50	0.40	110	12.7	0-10 (e), 25 (r)
14	BSDL126 (in LMC N79A)	4 51 53	-69 23 26	NC	0.65	0.50	140	8.2	-
14	IC2111, ESO56EN13, BRHT1b	4 51 51	-69 23 35	NC	0.65	0.55	130	7.2	2-3 (F), 3.7-4.3 (i)
	(in LMC N79A)
14	KMHK171 (in BRHT1a)	4 51 53	-69 24 24	NC	0.90	0.90	-	18.7	0-10 (e), 25 (r)
14	LMC-N79B (in NGC1722=BRHT1a)	4 52 00	-69 23 43	NC	0.40	0.35	140	18.1	0-10 (e), 25 (r)
15	BSDL129	4 51 56	-70 23 52	CA	0.40	0.35	70	7.4	-
15	SL66, KMHK180	4 51 55	-70 23 22	C	1.20	1.10	130	7.4	2000 - 5000 (e)
16	H88-11, H80F1-10	4 52 20	-68 59 32	AC	0.50	0.35	30	16.8	-
16	H88-7, H80F1-8	4 52 12	-69 00 26	AC	0.55	0.40	80	16.8	-
17	BSDL155 (in LMC DEM13)	4 53 13	-68 01 48	AC	0.50	0.40	130	19.9	-
17	HDE268680 (in NGC1736)	4 53 03	-68 03 06	NC	0.95	0.80	110	6.8	0-10 (e)
17	LMC-S6 (in NGC1736)	4 53 08	-68 03 05	NC	0.35	0.35	-	6.8	0-10 (e)
18	BSDL157 (in SGshell LMC7)	4 53 00	-69 38 42	AC	0.50	0.45	60	18.7	-
18	KMHK207 (in SGshell LMC7)	4 53 00	-69 37 25	C	0.75	0.75	-	18.7	-
19	BSDL158	4 53 09	-68 38 34	AC	0.50	0.50	-	7.1	-
19	NGC1732, SL77, ESO56SC17, KMHK209	4 53 11	-68 39 01	C	1.10	1.00	50	7.1	30 - 70 (e)
20	KMHK212 (in NGC1731)	4 53 35	-66 55 25	C	0.75	0.60	170	8.6	<4 (NGC1731) (G)
20	SL82, KMHK211 (in NGC1731)	4 53 29	-66 55 28	AC	0.85	0.60	100	8.6	<4 (NGC1731) (G)
21	BSDL162	4 53 24	-67 53 00	AC	0.55	0.55	-	19.1	-
21	HS56, KMHK218	4 53 36	-67 52 20	CA	0.75	0.70	50	19.1	-

(a): Banks et al. (1995): BV CMD and isochrone fitting
(b): Barbaro & Olivi (1991): UV spectra of the clusters and comparison with models
(c): Bhatia (1992): integrated BVR photometry
(d): Bhatia & Piotto (1994): BV CMD and isochrone fitting
(e): Bica et al. (1996): integrated UV photometry
(f): Caloi & Cassatella (1998): IUE spectra, CMD and evolutionary tracks
(g): Cassatella et al. (1996): integrated UV colours
(h): Chiosi et al. (1988): integrated UBV colours, synthetic HR diagrams, turn-off ages from Chiosi et al. (1986)
(i): Copetti et al. (1985): age estimates from [O III]/H $\beta$ for H II regions
(j): de Oliveira et al. (1998): ages from SWB types deduced from UBV colours in Alcaino (1978)
(k): Dieball & Grebel (1998): CMD and isochrone fitting
(l): Dieball et al. (2000): CMD and isochrone fitting
(m): Dieball & Grebel (2000): CMD and isochrone fitting
(n): Dirsch et al. (2000): Strömgren CCD photometry and isochrone fitting
(o): Elson & Fall (1988): integrated UBV colours
(p): Elson (1991): CMDs and isochrone fitting
(q): Fischer et al. (1993): BV CMD and isochrone fitting
(r): Fujimoto & Kumai (1997): ages from U-B, B-V TCDs and synthetic evolutionary models
(s): Geisler et al. (1997): $\delta T$ magnitude difference between turn-off and giant branch clump
(t): Gilmozzi et al. (1994): CMD and isochrone fitting
(u): Girardi et al. (1995): integrated UBV colours
(v): Hilker et al. (1995): Strömgren CCD photometry and isochrone fitting
(w): Kontizas et al. (1994): HR diagram and isochrone fitting
(x): Kontizas et al. (1993): integrated IUE spectra and stellar content
(y): Kubiak (1990): CMD and isochrone fitting
(z): Laval et al. (1994): H $\alpha$ observations, kinematical data
(A): Laval et al. (1992): H $\alpha$ observations, kinematical data
(B): Laval et al. (1986): VBLUW colours, isochrone and comparison with cluster of known age (NGC 6231)
(C): Lee (1992): UBVI photometry
(D): Meurer et al. (1990): UV colours as age indicator
(E): Oliva & Origlia (1998): IR spectra, age from Elson & Fall (1988)
(F): Santos et al. (1995): integrated blue-violet spectral evolution, Table 6
(G): Santos et al. (1995): from U-B calibration, Table 1
(H): Shull (1983): age from kinematic considerations
(I): Tarrab (1985): ages from H $\beta$ equivalent width ( $W_{\rm H}\beta$ )
(J): Testor et al. (1993): HR diagram
(K): Vallenari et al. (1994): CMD and isochrone fitting
(L): Vallenari et al. (1998): CMD and isochrone fitting
(M): Will et al. (1995): CCD photometry
(N): Piertzynski & Udalsky (2000a): BVI CCD data and isochrone fitting.

The remaining groups with more than one member age have internal age differences larger than 10 Myr. In a few cases, a group with four or more members could be subdivided into two groups with two (or more) coeval or nearly coeval clusters. Each subgroup was counted as a single group. In the real age distribution 46 groups were found that have internal age differences $\le$ 10 Myr. Please note that this number does not include the groups nos. 90, 94, 124, 135, 180, 184, 206, 211, 243, 428, and 456. These groups show larger internal age differences than our selection criterion of $\Delta t < 10$ Myr but are included in Fig. 11. In a way, these groups are borderline cases to our selection criterion, see the text above. For Fig. 14, we use the stringent selection criterion that can easily be applied to the groups with scrambled cluster ages and thus makes a direct comparison possible. However, the number of real groups that match this strict selection criterion is significantly larger (more than 3.5 times) than the expected number of groups if the clusters' ages are randomly distributed (46 groups found compared to 12.9 groups expected). The peaks at 100 Myr and 400 Myr in Fig. 11 are not seen in Fig. 14 for the real group age distribution. If the "borderline cases'' (see above) are not considered, then the age distribution shows peaks at 4 Myr, 10 Myr, 25 Myr, 63 Myr and 630 Myr, i.e., the two peaks at the older ages are shifted to the next younger and older bin, respectively. The distribution of group ages resulting from scrambled member ages in Fig. 14 is normalized so that the ordinate gives the number of groups in percent. For comparison the distribution of the real group ages is also plotted (solid line). As can be seen, the distribution based on the scrambled cluster ages (dotted line) is smoother with peaks at 4 Myr, 16 Myr, and 100 Myr. Only few groups are older than 200 Myr.

The lower diagram in Fig. 14 shows the deviation in age for the group ages. The solid line represents the deviation for the real group ages: $\approx$ 70% of all groups show no or a very small age deviation (smaller than 0.5 Myr), and the mean sigma is about $1.0\pm2.0$ Myr. In contrast, the deviation for the group ages based on the scrambled cluster ages (dotted line) is smoother, i.e., fewer groups have smaller ( $\approx$ 35%) and more groups have larger deviations than 0.5 Myr when compared to the real group age deviations. The mean deviation for the group ages based on the mixed cluster ages is $2.7\pm2.6$ Myr and thus larger than the mean internal scatter for the real group ages. If only groups are considered with $\sigma(t)>0.5$ Myr, the mean sigma is $3.2\pm2.4$ Myr for the real distribution and $4.1\pm2.2$ Myr for the groups with scrambled cluster ages.

In Fig. 15 we plotted the ages found for the clusters versus the separations that the clusters have within the groups (upper diagram), and the group ages versus their internal mean separations (middle diagram). No correlation can be seen from Fig. 15. Thus we cannot draw any conclusions whether older groups or group components tend to have larger (mean) separations, which would indicate that the components of the multiple cluster are drifting apart, or whether older clusters have smaller separations, which might indicate that the system will undergo a merging process. Both processes could be equally likely, which might explain why we see no tendency towards larger or smaller separations. The lower diagram of Fig. 15 displays the groups' internal age scatter versus their internal mean separation. There might be a tendency towards larger age scatter with larger mean separations (which indicates larger groups), but if so, it is only weak. Note that we took "all'' groups into account whose components agree within the errors of their age determination with a common formation, i.e., groups nos. 90, 94, 124, 135, 180, 184, 206, 211, 243, 428, and 456 are included. The data point at $\sigma({\rm age}) \approx 36$ Myr belongs to group no. 206 whose components differ in age by 50 Myr, but considering their age of 500 Myr and 450 Myr, both clusters agree within the errors with a common formation. Efremov & Elmegreen (1998) proposed that close clusters in pairs have more similar ages. The pairs' average age differences increase with increasing separations between the clusters. However, the authors do not restrict their study to binary cluster candidates that have separations of 20 pc ( $1\farcm4$ ) or smaller. Indeed, their Fig. 1 seems to indicate that only very few binary cluster candidates but pairs with much larger distances were considered. However, we cannot confirm the strong tendency suggested by Efremov & Elmegreen (1998).

6 Properties of the multiple clusters

6.1 Separations between the components of the cluster pairs

6.2 Size distribution

6.3 Spatial distribution of the cluster pairs and groups

6.4 Ages of the binary and multiple cluster candidates