The determination of the critical point of the q-state Potts model on the Kagom´ e lattices has been an outstanding unsolved problem. Here we study this problem by regarding the Potts model as generating correlated bond percolations. By applying a combination of Monte Carlo renormalization group and finite-size scaling analyses to the percolation problem, numerical estimates with an accuracy of 0:01% are obtained for the Kagomcritical point for q D 1; 2; 3; 4. Our results for q D 1 are consistent with a recent highly accurate numerical estimate by Ziff and Suding, and results for q D 2 agree with the known exact result within the numerical accuracy. Compared with results obtained in a recent series analysis by Jensen et al, our numbers differ from theirs slightly for q D 3, and agree with theirs with a slightly better accuracy for qD 4. Our numbers also confirm that a conjecture due to Wu is extremely accurate.