2002 AMC 12A Problem 6

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

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.