We consider the preconditioned conjugate gradient (PCG) method for solving the linear equations derived from difference approximations to the Laplace operator on 1D line, 2D square or 3D cube domains. If the preconditioner is a block diagonal matrix obtained from cutting the original domain by lines or planes, we can End an upper bound for the condition number of the preconditioned system. For several different parallel machine models, we derive the optimal number of processors to achieve the best asymptotic run time.