In this work we study the Capacitated p-Center Problem (CpCP) and we propose an exact algorithm to solve it. We study two auxiliary problems and their relation to CpCP, and we propose two different Lagrangean duals based on each of the auxiliary problems. The lower and upper bounds provided by each of the Lagrangean duals reduce notably the set of candidate radii and allow to solve the problem with an exact algorithm based on binary search. The results obtained with experimental testing on various data sets from literature show the efficiency of the proposal that outperforms previous proposals.