imc

This is a Pythagorean triple (a $3-4-5$ actually) with legs $15$ and $20$. The area is then $\frac{(15)(20)}{2}=150$. Now, consider an altitude drawn to any side. Since the area remains constant, the altitude and side to which it is drawn are inversely proportional. To get the smallest altitude, it must be drawn to the hypotenuse. Let the length be $x$; we have $\frac{(x)(25)}{2}=\frac{(15)(20)}{2}$, so $25x=300$ and $x$ is 12. Our answer is then $\boxed{12}$.