In this work we have considered the dynamic scaling relation of the magnetization in order to study the dynamic scaling behavior of 2- and 3-dimensional Ising models. We have used the literature values of the magnetic critical exponents to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. In this way we have calculated the dynamic critical exponent Z for 2- and 3-dimensional Ising Models by using the Swendsen-Wang cluster algorithm. We have also presented that this method opens the possibility of calculating z and x(0) separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling. (C) 2006 Elsevier B.V. All rights reserved.