AMC 12 2010b Problem 25

For every integer $n\ge2$, let $\text{pow}(n)$ be the largest power of the largest prime that divides $n$. For example $\text{pow}(144)=\text{pow}(2^4\cdot3^2)=3^2$. What is the largest integer $m$ such that $2010^m$ divides

\textbf{(A)}\ 74 \textbf{(B)}\ 75 \textbf{(C)}\ 76 \textbf{(D)}\ 77 \textbf{(E)}\ 78