The face-centered-cubic (fcc) Lennard-Jones (LJ) model can be considered as a representative model of a simple solid. We investigate the mechanism of melting at the limit of superheating in the fcc LJ solid by means of the procedure recently developed by us [Phys. Rev. B 73, 012201 (2006)]. Insight into the mechanism of melting was gained by studying diffusion and defects in the fcc LJ solid by means of molecular dynamics simulations. We found that the limit of superheating achieved by us is likely to be the highest so far. We also found that the size of the cluster which ignites the melting is very small (down to five to six atoms, depending on the size of the supercell) and closely correlates with the linear size of a supercell when the number of atoms varies between 500 and 13 500.