Question

if two positive integers p and q are written as p=a^2 b^3 and q=a^3 b; a,bare prime numbers then verify lcm (p,q)×hcf (p,q)=pq

Answer 1

Here the lcm(a²b³,a³b)
Is a³b³( highest power is the lcm)
And the hcf (a²b³,a³b)
Is a²b ( lowest power is the hcf)
Now
Hcf*lcm=p*q
a²b*a³b³=a²b³*a³b
a^5*b⁴=a^5*b⁴
Hence proved