Question

If two positive integers $p$ and $q$ are written as $p=a^2{b}^2$ and $q=a^{3}b$, a,b are prime numbers then verify that $L.C.M.(p,q)\times H.C.F.(p,q)=pq$

Answer 1

$H.C.F.\left(p,q\right)=a^{2}b$

$L.C.M.\left(p,q\right)=a^3{b}^2$

$L.C.M.\left(p,q\right)\times H.C.F.\left(p,q\right)=a^5{b}^3$

$pq=a^5{b}^3$

Therefore, $L.C.M.\left(p,q\right)\times H.C.F.\left(p,q\right)=pq$.