AMC 12 2002a Problem 6

For how many positive integers $m$ does there exist at least one positive integer $n$ such that $m \cdot n \le m + n$?

$\mathrm{(A) \ } 4 \mathrm{(B) \ } 6 \mathrm{(C) \ } 9 \mathrm{(D) \ } 12 \mathrm{(E) \ }$ infinitely many