SFHs predicted by Vasini et al. (2022, 2023) and used in the paper. For the MW (red line), the Kennicutt (1998) law with exponent k = 1.5 was adopted, and the temporal evolution of the star formation at the solar ring (8 kpc) is compared with the present-day observed SFR (vertical yellow line, data taken from Prantzos et al. 2018). For the LMC (blue line) we assumed a linear Kennicutt (1998) law with a variable efficiency to reproduce the Harris & Zaritsky (2009) SFR. We compared it with the observation at the present time by Harris & Zaritsky (2009) itself (vertical cyan line).