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
(A) $ab$
(B) $a^2b^2$
(C) $a^3b^2$
(D) $a^3b^3$

Given: 

Two positive integers $p$ and $q$ can be expressed as $p = ab^2$, and $q = a^3b; a, b$ being prime numbers.

To find: 

Here we have to find LCM $(p, q)$.

Solution:

We know that,

LCM is the product of the greatest power of each prime factor involved in the numbers.

$p = ab^2$

$= a \times b^2$

$q = a^3b$

$= a^3 \times b$

Therefore,

LCM of $p$ and $q$ is,

LCM $(ab^2, a^3b) = b^2 \times a^3$

$= a^3b^2$

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Updated on: 10-Oct-2022

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