Question

If two positive integer p and q are written as p=asquare× bcube and q=acube×b,,a and b are prime number then verify that LCM(p,q)×HCF(p,q)=p×q??

Answer 1

p=a²b³

q=a³b

LCM(p,q)=a³b³

HCF(p,q)=a²b

now,LHS

LCM(p,q)×HCF(p,q)

a³b³×a²b

$= {a}^{5} {b}^{4}$


now,LHS

p×q

a²b³×a³b


$= {a}^{5} {b}^{4}$

since,LHS=RHS
hence,verified!!