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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 (a)`p q` (b) `p^3q^3` (c) `p^3q^2` (d) `p^2q^2`

A

`pq`

B

`p^(2)q^(2)`

C

`p^(3)q^(2)`

D

`p^(3)q^(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
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]
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