  The least squares solutions with the minimum norm of the matrix equations
${\rm {\bf A}}{\rm {\bf X}} = {\rm {\bf B}}$, ${\rm {\bf X}}{\rm {\bf A}} =
{\rm {\bf B}}$ and ${\rm {\bf A}}{\rm {\bf X}}{\rm {\bf B}} ={\rm {\bf D}} $
are considered in this paper. We use the determinantal representations of the
Moore - Penrose inverse obtained earlier by the author and get analogs of the
Cramer rule for the least squares solutions of these matrix equations.
