The blocks of masses $m$ and $M$ are not attached. The coefficient of static friction between the blocks is $\mu$, but the surface beneath $M$ is smooth. What is the maximum magnitude of the horizontal force $F$ required to hold it against $M$:

              $F-N =ma .............\left(i\right)$

and        $N = Ma$

              $a = \left[\frac{F}{M+m}\right] ..........\left(ii\right)$

For block m remains stationary w.r.t $M$, then

                                $\mu N =mg ..............\left(iii\right)$

Solving above equations, we get

                                $F = \left[\frac{m\left(M+m\right)g}{\mu M}\right]$