Question 7

If two positive integers $a$ and $b$ are expressible in the form $a=p{q}^2$ and $b=p^{3}q$ ; $p,q$ being prime numbers, then LCM $(a,b)$ is

Solution:

Given that $p=a{b}^2=a\times b\times b$
and $q=a^{3}b=a\times a\times a\times b$
$\therefore$ LCM of p and q=LCM $(a{b}^2,a^{3}b)=a\times b\times ba\times a=a^3{b}^2$
[Since, LCM is the product of the greatest power of each prime factor involved in the number]