2000 AMC 12 Problem 1

In the year 2001, the United States will host the International Mathematical Olympiad. Let I,M, and O be distinct positive integers such that the product I \cdot M \cdot O = 2001. What is the largest possible value of the sum I + M + O?

\textbf{(A)}\ 23 \qquad \textbf{(B)}\ 55 \qquad \textbf{(C)}\ 99 \qquad \textbf{(D)}\ 111 \qquad \textbf{(E)}\ 671

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