Question

Question 7
If two positive integers p and q can be expressed as p = $a{b}^{2}andq=a^{3}b$; where a, b being prime numbers, then LCM (p, q) is equal to

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

Answer 1

The answer is C.
Given that, $p=a{b}^2=a\times b\times b$
$q=a^{3}b=a\times a\times a\times b$

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

$\therefore$ LCM of p and q = LCM $(a{b}^2,a^{3}b)=a\times a\times a\times b\times b=a^3{b}^2$