Question 75
Let gcd mean the greatest common divisor of two numbers and lcm their least common multiple. Suppose the three numbers $A$, $B$, $C$ satisfy
$$
\begin{array}{ll}
\operatorname{gcd}(A, B)=2, & \operatorname{lcm}(A, B)=60 \\
\operatorname{gcd}(A, C)=3, & \operatorname{lcm}(A, C)=42
\end{array}
$$
Determine the three numbers.
$$
\begin{array}{ll}
\operatorname{gcd}(A, B)=2, & \operatorname{lcm}(A, B)=60 \\
\operatorname{gcd}(A, C)=3, & \operatorname{lcm}(A, C)=42
\end{array}
$$
Determine the three numbers.