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. 

$\{x,y\} \subset \{2,3,5,7\}$
$10x + 2$ and $10x + 5$ are not prime.  $5 + 7 = 12 = 3*4;2+7 = 9=3*3 $ so $57,75,27,72$  are not prime.  So possible contenders are.
$(x,y, 10x+y): = (7,3,73),(3,7,37),(5,3,53), (2,3,23)$.
$7*3*73 > 21*70 > 1400$ and not three digits.
Clearly $2< 3, 3 < 5 < 7$ and $23< 37< 53$ so $(2,3,23)$ is out.
$7*37$ and $5*53$ and similar in size so it will be either $3*7*37$ or $5*3*53$ depending upon whether $7*37 = 210 + 49$ is more or less than $5*53 = 250 +15$.
