2011 AMC 12B Problem 5

Let N be the second smallest positive integer that is divisible by every positive integer less than 7. What is the sum of the digits of N?

\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 5 \qquad \textbf{(D)}\ 6 \qquad \textbf{(E)}\ 9

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