2002 AMC 12P Problem 3

The dimensions of a rectangular box in inches are all positive integers and the volume of the box is 2002 in^3. Find the minimum possible sum of the three dimensions.

\text{(A) }36 \qquad \text{(B) }38 \qquad \text{(C) }42 \qquad \text{(D) }44 \qquad \text{(E) }92

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