2002 Cayley Problem 16

If the product of four consecutive positive integers is 358\,800, then the sum of these four integers is

\textbf{(A)}\ 102\quad \textbf{(B)}\ 98\quad \textbf{(C)}\ 94\quad \textbf{(D)}\ 90\quad \textbf{(E)}\ 106

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.