What type of objects are being detected as $zsim 3$ Lyman break galaxies? Are they predominantly the most massive galaxies at that epoch, or are many of them smaller galaxies undergoing a short-lived burst of merger-induced star formation? We attempt to address this question using high-resolution cosmological hydrodynamic simulations including star formation and feedback. Our $Lambda$CDM simulation, together with Bruzual-Charlot population synthesis models, reproduces the observed number density and luminosity function of Lyman break galaxies when dust is incorporated. The inclusion of dust is crucial for this agreement. In our simulation, these galaxies are predominantly the most massive objects at this epoch, and have a significant population of older stars. Nevertheless, it is possible that our simulations lack the resolution and requisite physics to produce starbursts, despite having a physical resolution of $la 700$ pc at z=3. Thus we cannot rule out merger-induced starburst galaxies also contributing to the observed population of high-redshift objects.