44. Find a two-digit number that is equal to three times the product of its digits.
44. $x$ is the number of tens, $y$ is the number of units of the desired number, then $10 x+y=3 x y$, $x=\frac{y}{3 y-10}$. Since $x>0, y>0$, then $3 y-10>0, y>\frac{10}{3}$. But $x$ is an integer, therefore, $y \geqslant 3 y-10$, from which $y \leqslant 5$. Thus, $\frac{10}{3}<y \leqslant 5$. Therefore, $y=4, x=2$ or $y=5, x=1$. Answer: 24 and 15.