Question

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is ______.

Options

• ab

• a²b²

• a³b²

• a³b³

Answer 1

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is `underline(bb(a^3b^2))`.

Explanation:

Given that, p = ab² = a × b × b

And q = a³b = a × a × a × b

LCM of p and q = LCM (ab², a³b)

= a × b × b × a × a

= a³b²    .........[Since, LCM is the product of the greatest power of each prime factor involved in the numbers]