jmc

For an integer to have only two positive divisors, it must be prime (the only positive divisors of a prime number are $1$ and itself). Since $2$ is the smallest positive prime, $m=2$. For a positive integer to have exactly three positive divisors, it must be in the form $p^2$ where $p$ is prime (its only factors would be $1$, $p$, and $p^2$). The largest $p^2$ less than $100$ is $7^2=49$. Thus, $n=49$ and $m+n=2+49=\boxed{51}$.