The main purpose of the study is to perform parallel computing for k-means clustering on estimating the underlying latent class process. OpenMP and MPI parallel computing make computing time shorter for updated and non-updated k-means clustering method. We compare the parallel efficiency of OpenMP and MPI in the personal computers, the national center for high-performance computing and the Amazon EC2 environment. Besides, the breast cancer microarray data are used for illustration. The results display that parallel computing can reduce the computation time in all three computing environments.