Different LG mass estimates. Panel a: Observational estimates of the LG mass from the LG Hubble-Lemaître flow (blue shaded region; Peñarrubia et al. 2014) and momentum balancing (Diaz et al. 2014). The sum of the MW (Jiao et al. 2023) and M31 (Hammer et al. 2025) mass from their rotation curves with the CGM (Wang et al. 2019) and IGM (McConnachie et al. 2007) mass is also shown. Panel b: TA mass with the M31 PMs from Gaia DR3 (Rusterucci et al. 2024) and HST (van der Marel et al. 2012). Panel c: TA calculation with the M31 merger correction and the M31 PM fixed for the minimum mass. Three sets of TA calculations are shown: without LMC corrections, with disc-sloshing corrections (Chamberlain et al. 2022), and with corrections using LMC infall simulations (Benisty et al. 2022). Panel d: Expected TA mass assuming 16 major mergers for each galaxy.