  This article compares the distribution of Ks magnitude of Large Magellanic
Cloud (LMC) asymptotic giant branch (AGB) stars obtained from the DENIS and
2MASS data with theoretical distributions. These have been constructed using
up-to-date stellar evolution calculations for low and intermediate-mass stars,
and in particular for thermally pulsing AGB stars. A fit of both the magnitude
distribution of carbon- and oxygen-rich AGB stars allowed us to constrain the
metallicity distribution across the LMC and its star formation rate (SFR). The
LMC stellar population is found to be on average 5-6 Gyr old and is consistent
with a mean metallicity corresponding to Z=0.006. These values may however be
affected by systematic errors in the underlying stellar models, and by the
limited exploration of the possible SFR histories. Our method should be,
instead, particularly useful for detecting variations in the mean metallicity
and SFR across the LMC disk. In fact, there are well defined regions where both
the metallicity and the mean-age of the underlying stellar population span the
whole range of grid parameters. The C/M ratio discussed in paper I is a tracer
of the metallicity distribution if the underlying stellar population is older
than about a few Gyr. A similar study across the Small Magellanic Cloud is
given in paper III of this series.
