The physical properties of a series of asymmetric binary Lennard-Jones mixtures are studied using effective one-component simulations. The degrees of freedom of the smaller Lennard-Jones component are rigorously integrated out to give an expression for the Hamiltonian of the effective (coarse-grained) large Lennard-Jones sphere system. The coarse-grained Hamiltonian is comprised of a series of 0, 1, 2,...,N-body terms which we truncate at the 2-body term. Various thermodynamic and structural properties of the coarse-grained systems are computed and compared with the corresponding 2-component system properties to assess the effect of neglecting 3-body and higher terms in the coarse-grained potential. We also examine the state point dependence of the coarse-grained potentials.