The product of three different positive integers is 72 . What is the smallest possible sum of these integers?
(A) 13
(B) 14
(C) 15
(D) 17
(E) 12

## Part C: Each correct answer is worth 8.
The possible ways of writing 72 as the product of three different positive integers are: $1 \times 2 \times 36$; $1 \times 3 \times 24 ; 1 \times 4 \times 18 ; 1 \times 6 \times 12 ; 1 \times 8 \times 9 ; 2 \times 3 \times 12 ; 2 \times 4 \times 9 ; 3 \times 4 \times 6$.

(We can find all of these possibilities systematically by starting with the smallest possible first number and working through the possible second numbers, then go to the next possible smallest first number and continue.)

The sums of these sets of three numbers are $39,28,23,19,18,17,15,13$, so the smallest possible sum is 13 .

ANSWER: (A)