AMC 12 2011b 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 \textbf{(B)}\ 4 \textbf{(C)}\ 5 \textbf{(D)}\ 6 \textbf{(E)}\ 9