Let $a$ and $b$ be two positive integers such that $a=p^{3} q^{4}$ and $b=p^{2} q^{3}$, where $p$ an

Question

Let $a$ and $b$ be two positive integers such that $a=p^{3} q^{4}$ and $b=p^{2} q^{3}$, where $p$ and $q$ are prime numbers. If $\operatorname{HCF}(a, b)=p^{m} q^{n}$ and $\operatorname{LCM}(a, b)=p^{r} q^{s}$, then ( $m+n$ ) $(r+s)=$\

Professor PC Thomas Classes · Answer

(c): Given $a=p^{3} q^{4}$ and $b=p^{2} q^{3}$\ $	herefore \quad \operatorname{LCM}(a, b)=p^{3} q^{4}$ and $\operatorname{HCF}(a, b)=p^{2} q^{3}$\ Comparing the obtained LCM and HCF with the given LCM and HCF, we get\ $m=2, n=3, r=3$ and $s=4$ \ $	herefore (m+n) (r+s) = 5 	imes$ 7  = 35...(1)