In the multiplication magic square below, $l, m, n, p, q, r, s, t, u$ are positive integers. The product of any three numbers in any row, column or diagonal is equal to a constant $k$, where $k$ is a number between $11, 000$ and $12, 500$. Find the value of $k$. \begin{tabular}{|l|l|l|} \hline $l$ & $m$ & $n$ \\ \hline $p$ & $q$ & $r$ \\ \hline $s$ & $t$ & $u$ \\ \hline \end{tabular}