The miscibility behavior of binary mixtures of polymeric and low molecular weight molecules was studied using a combination of modified Flory-Huggins theory and molecular simulation techniques. Three different atomistic approaches were used to investigate the phase behavior and chi parameters of binary mixtures consisting of polymethyl methacrylate (PMMA) and 4-n-pentyl-4'-cyanobiphenyl (5CB). Binary mixtures of methyl methacrylate monomer/5CB and methyl methacrylate oligomer/5CB were also studied. As a first approach, a fast method that calculates the local interaction between a fragment of the polymer and the organic molecule and then extends it to determine the energy of mixing using an estimated coordination number was used. By using modified coordination numbers, we were able to extend this method to include cases where the polymer segment and the small molecules are slightly dissimilar in size. More detailed studies which take into account bulk effects were also carried out where the cohesive energies of the pure compounds were derived from molecular dynamics simulations and the interaction parameters were determined from the differences in the cohesive energies. The concentration and temperature dependence of the chi parameters was evaluated by calculating the energy of mixing from the differences in the cohesive energy densities of the mixed and demixed systems. The present study provides a detailed understanding of the miscibility of PMMA and 5CB as PMMA polymerizes from its monomer, and the results indicate that although methyl methacrylate and 5CB are completely miscible, 5CB is not miscible in PMMA even in small quantities.