We seek to quantify the relative contributions of Lorentz forces and aerodynamic drag on the propagation of solar coronal mass ejections (CMEs). We use Graduated Cylindrical Shell (GCS) model fits to a representative set of 38 CMEs observed with the SOHO and STEREO spacecraft. We find that the Lorentz forces generally peak between 1.65 and 2.45 Rsun for all CMEs. For fast CMEs, Lorentz forces become negligible in comparison to aerodynamic drag as early as 3.5-4 Rsun. For slow CMEs, however, they become negligible only by 12-50 Rsun. For these slow events, our results suggest that some of the magnetic flux might be expended in CME expansion or heating. In other words, not all of it contributes to directed propagation. Our results are expected to be important in building a physical model for understanding the Sun-Earth dynamics of CMEs.