2000 Cayley Problem 14

A positive integer is to be placed in each box. The product of any four adjacent integers is always 120. What is the value of x?

\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \phantom{x} & \phantom{x} & 2 & \phantom{x} & \phantom{x} & 4 & \phantom{x} & \phantom{x} & x & \phantom{x} & \phantom{x} & 3 & \phantom{x} & \phantom{x} \\ \hline\end{array}

\textbf{(A)}\ 1\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ 3\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 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.