The volume of a rectangular prism is 21 . Its length, width and height are all different positive integers. The sum of its length, width and height is
(A) 11
(B) 13
(C) 15
(D) 9
(E) 17
Suppose that the length, width and height of the prism are the positive integers $a, b$ and $c$. Since the volume of the prism is 21 , then $a b c=21$.

We note that each of $a, b$ and $c$ is a positive divisor of 21 .

The positive divisors of 21 are 1, 3, 7, and 21, and the only way to write 21 as a product of three different integers is $1 \times 3 \times 7=21$.

Therefore, the length, width and height of the prism must be 1,3 , and 7 , in some order.

The sum of these is $1+3+7=11$.

ANswer: (A)