CMO 2002 Problem 2

Call a positive integer $n$ practical if every positive integer less than or equal to $n$ can be written as the sum of distinct divisors of $n$.

For example, the divisors of 6 are $\mathbf{1 , 2}, \mathbf{3}$, and $\mathbf{6}$. Since

$$1=\mathbf{1}, 2=\mathbf{2}, 3=\mathbf{3}, 4=\mathbf{1}+\mathbf{3}, 5=\mathbf{2}+\mathbf{3}, 6=\mathbf{6},$$

we see that 6 is practical.

Prove that the product of two practical numbers is also practical.