The Magellanic Mopra Assessment (MAGMA) is a high angular resolution 12CO (J= 1 → 0) mapping survey of giant molecular clouds (GMCs) in the Large Magellanic Cloud (LMC) and Small Magellanic Cloud using the Mopra Telescope. Here we report on the basic physical properties of 125 GMCs in the LMC that have been surveyed to date. The observed clouds exhibit scaling relations that are similar to those determined for Galactic GMCs, although LMC clouds have narrower linewidths and lower CO luminosities than Galactic clouds of a similar size. The average mass surface density of the LMC clouds is 50 M⊙ pc−2, approximately half that of GMCs in the inner Milky Way. We compare the properties of GMCs with and without signs of massive star formation, finding that non-star-forming GMCs have lower peak CO brightness than star-forming GMCs. We compare the properties of GMCs with estimates for local interstellar conditions: specifically, we investigate the H i column density, radiation field, stellar mass surface density and the external pressure. Very few cloud properties demonstrate a clear dependence on the environment; the exceptions are significant positive correlations between (i) the H i column density and the GMC velocity dispersion, (ii) the stellar mass surface density and the average peak CO brightness and (iii) the stellar mass surface density and the CO surface brightness. The molecular mass surface density of GMCs without signs of massive star formation shows no dependence on the local radiation field, which is inconsistent with the photoionization-regulated star formation theory proposed by McKee. We find some evidence that the mass surface density of the MAGMA clouds increases with the interstellar pressure, as proposed by Elmegreen, but the detailed predictions of this model are not fulfilled once estimates for the local radiation field, metallicity and GMC envelope mass are taken into account.