2006 AMC 12B Problem 22

Suppose a, b and c are positive integers with a+b+c=2006, and a!b!c!=m\cdot 10^n, where m and n are integers and m is not divisible by 10. What is the smallest possible value of n?

\mathrm{(A)}\ 489 \qquad \mathrm{(B)}\ 492 \qquad \mathrm{(C)}\ 495 \qquad \mathrm{(D)}\ 498 \qquad \mathrm{(E)}\ 501

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