This work aims at presenting a general approach to locate azeotropic points in multicomponent polymerizations. Typically, for azeotropy studies in ternary systems, the literature is dominated by graphical solutions which may only be approximate. The approach consists of obtaining an azeotropic composition through a direct numerical solution of the relevant terpolymerization composition equations. The numerical approach is capable of locating the correct azeotropic composition for any ternary or multicomponent system, if such a point exists, and is illustrated via three case studies. Compared to prior efforts for azeotropic composition calculations in the literature, the presented numerical approach can be considered as general, direct, reliable, and more straightforward.