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} multiplicationcombinatorics