If two positive integers p and q can be expressed as \(p = ab^2\) and \(q = a^3b\); \(a, b\) being prime numbers, then \(LCM(p, q)\) is
\(ab\)
\(a^2b^2\)
\(a^3b^2\)
\(a^3b^3\)
The LCM is found by taking the highest power of each prime factor from both numbers.
For \(a\), the powers are \(1\) (in p) and \(3\) (in q). The maximum is \(3\).
For \(b\), the powers are \(2\) (in p) and \(1\) (in q). The maximum is \(2\).
So, the LCM is \(a^3b^2\).