three distinct prime factors $x$, $y$ and $10x+y$, where $x$ and $y$ are each less than 10. What is the largest possible value of $m$? The number $m$ is a three-digit positive integer and is the product of the three distinct prime factors $x$, $y$ and $10x+y$, where $x$ and $y$ are each less than 10. What is the largest possible value of $m$?
Any hints are greatly appreciated. 

It isn't too hard here to simply brute force, with some optimization. Note $y \neq 2, 5$, as that would lead to $10x + y$ being nonprime. Now, let's consider the pairs of $(x, y)$ that do work. These pairs are: (2, 3); (3, 7); (5, 3); (7, 3). I assume you can proceed from here.
