Question

If two positive integers p and q are written as p = a2b3 and q = a3b; a, b are primenumbers, then verify: lcm (p, q) × hcf (p, q) = pq

Answer 1

Given :- p = a²b³
:- q = a³b


• HCF :- Product of the smallest power of each common prime factor in the number.


So,

HCF ( p , q ) = a² b


• LCM :- Product of the greatest power of each prime factors involved in the number.


So,

LCM ( p , q ) = a³b³



We have to verify :-

LCM ( p , q ) × HCF ( p , q )= product of pq


Taking LHS

LCM ( p , q ) × HCF ( p , q )

a³b³ × a²b


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



Now,

Taking RHS


Product of pq

a²b³ × a³b



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



Since LHS = RHS

Hence verified !!


@Altaf

Answer 2

Answer:

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Step-by-step explanation:

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