If two positive integers `m` and `n` are expressible in the form `m=p q^3` and `n=p^3q^2` , where `p ,\ q` are prime numbers, then HCF `(m ,\ n)=`

Options

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

Answer

B

Explanation

Given that `a-x^(3)y^(2)=x xx x xx x xx y xx y`
and `b=xy^(3)= x xx y xx y xx y`
`therefore HCF` of a and b `=HCF(x^(2)y^(2),xy^(3))=x xx y xx y=xy^(2)`
[Since, HCF is the product of the smallest power of each common prime facter involed is the number]