Kinetic Monte Carlo (KMC) has become a well-established technique for simulating the kinetics of free radical polymerization, both to generate polymer molecular weight distributions and, more recently, to track the explicit monomer sequence in every chain. However, KMC simulations require a minimal number of molecules in order to accurately describe monomer conversion and macromolecular quantities, which can render them computationally prohibitive. In this work, we propose a novel approach for accelerating KMC simulations through scaling relationships that allow the number of molecules simulated to be reduced. Using the concept of the minimal number of molecules and an explicit expression we derived for copolymerization, we propose a factor that is used to scale the reaction rate constants which results in an acceleration of KMC simulations by a factor of similar to 100. Furthermore, we demonstrate the limits of this scaling approach, revealing the absolute lower bound for the number of molecules used in KMC simulations of free radical polymerization and the associated population size of dead chains formed. We illustrate this approach using examples of acrylate copolymerization, but this approach is sufficiently general that it can be applied to a wide variety of free radical polymerization systems and even other free radical chemistries.