2009 Cayley Problem 8

When three consecutive positive integers are multiplied together, the answer is always

\textbf{(A)} odd \textbf{(B)} a multiple of 6 \textbf{(C)} a multiple of 12 \textbf{(D)} a multiple of 4 \textbf{(E)} a multiple of 5

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.