In this paper, the algorithm Largest Gaps is introduced, for simultaneously clustering both rows and columns of a matrix to form homogeneous blocks. The definition of clustering is model-based: clusters and data are generated under the Latent Block Model. In comparison with algorithms designed for this model, the major advantage of the Largest Gaps algorithm is to cluster using only some marginals of the matrix, the size of which is much smaller than the whole matrix. The procedure is linear with respect to the number of entries and thus much faster than the classical algorithms. It simultaneously selects the number of classes as well, and the estimation of the parameters is then made very easily once the classification is obtained. Moreover, the paper proves the procedure to be consistent under the LBM, and it illustrates the statistical performance with some numerical experiments.