If two positive integers m and n are expressible in the form m
Question:

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

(a) $p q$

(b) pq2

(c) $p^{3} q^{2}$

(d) $p^{2} q^{2}$

Solution:

Two positive integers are expressed as follows:

$m=p q^{3}$

$n=p^{3} q^{2}$

p and q are prime numbers.

Then, taking the smallest powers of and q in the values for m and n we get

$\operatorname{HCF}(m, n)=p q^{2}$

Hence the correct choice is (b).