13. Find all positive integer pairs $(a, b)$ that satisfy $(a, b)=10,[a, b]=100$.
13. $(a / 10, b / 10)=1,[a / 10, b / 10]=10 . a / 10, b / 10$ can only take the values $1,2,5,10$, and satisfy the above conditions. Therefore, we get the following table:
\begin{tabular}{|c|cccc|}
\hline$a / 10$ & 1 & 10 & 2 & 5 \\
\hline$b / 10$ & 10 & 1 & 5 & 2 \\
\hline
\end{tabular}