Smallest third number for a given lcm

You are given three integers $a$, $b$, and $L$. Find the smallest positive integer $c$ such that $\operatorname{lcm}(a, b, c) = L$, where $\operatorname{lcm}(a, b, c)$ is the least common multiple of $a$, $b$, and $c$.

The first line contains $a$, $b$, and $L$, separated by spaces. ($1 \le a, b \le 10^6$, $1 \le L \le 10^{12}$)

Print the smallest $c$ that satisfies the condition. If no such $c$ exists, print $-1$.