  We present a detailed analysis of the uncertainty on the theoretical
population corrections to the LMC Red Clump (RC) absolute magnitude, by
employing a population synthesis algorithm to simulate theoretically the
photometric and spectroscopic properties of RC stars, under various assumptions
about the LMC Star Formation Rate (SFR) and Age Metallicity Relationship (AMR).
A comparison of the outcome of our simulations with observations of evolved
low-intermediate mass stars in the LMC allows one to select the combinations of
SFR and AMR that bracket the real LMC star formation history, and to estimate
the systematic error on the associated RC population corrections.
  The most accurate estimate of the LMC distance modulus from the RC method
(adopting the OGLE-II reddening maps for the LMC) is obtained from the K-band
magnitude, and provides (m-M)_{0, LMC}=18.47 +/-0.01(random)
+0.05/-0.06(systematic). Distances obtained from the I-band, or from the
multicolour RC technique which determines at the same time reddening and
distance, both agree (albeit with a slightly larger error bar) with this value.
