Question 22
Paulinho was studying the maximum common divider (MDC) at school and decided to practice at home. He called $a, b$ and $c$ the ages of three people who live with him. He then did some operations with their prime factors and obtained the maximum common divisors of the 3 pairs of numbers. A few days later, he forgot the ages $a, b$ and $c$, but found the following results noted: $$
\begin{aligned}
a \cdot b \cdot c & =2^{4} \cdot 3^{2} \cdot 5^{3} \\
M D C(a, b) & =15 \\
M D C(a, c) & =5 \\
M D C(b, c) & =20
\end{aligned}
$$ Help Paulinho determine the values of $a, b$ and $c$.
\begin{aligned}
a \cdot b \cdot c & =2^{4} \cdot 3^{2} \cdot 5^{3} \\
M D C(a, b) & =15 \\
M D C(a, c) & =5 \\
M D C(b, c) & =20
\end{aligned}
$$ Help Paulinho determine the values of $a, b$ and $c$.