Question

If two positive integers p and q are written as p=a2b3 and q=a3b and a and b are prime numbers then verify: LCM(p,q)multiplies HCF(p,q)

Answer 1

Given :-

p = a²b³

q = a³b

LCM (p,q ) = a³b³

HCF ( p,q ) = a²b

Now taking LHS,

that is ,

LCM(p,q) × HCF(p,q)

= a³b³×a²b

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

Now by taking RHS,

that is product of pq

a²b³×a³b

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

Since, LHS = RHS

proved.

Answer 2

lcm of pand q=a3b
hcf of pand q=a2b3
so
lcm*hcf=a^5b^4
=p*q
hence proved
plz mark it as a brainlist answer