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

Options

A. `pq`
B. `p^(2)q^(2)`
C. `p^(3)q^(2)`
D. `p^(3)q^(3)`

Answer

C

Explanation

Given that `p=ab^(2)=a xx b xx b`
and `q=a^(3)b=a xx a xx a xx b`
`therefore` LCM of p and q=LCM `(ab^(2), a^(3)b)=a xx b xx b a xx a =a^(3) b^(2)`
[Since, LCM is the product of the greatest power of each prime factor involved in the number]