Question

If two positive integers P and Q are written as P=A² B³and Q=A³b, A, B are prime numbers, then Verify LCM (p,q)× HCF (p, q) =pq ?

Answer 1

Hi ,

p = a²b³

q = a³b

HCF ( p,q ) = a²b

[ ∵Product of the smallest power of each

common prime factors in the numbers ]

LCM ( p , q ) = a³b³

[ ∵ Product of the greatest power of each

prime factors , in the numbers ]

Now ,

HCF ( p , q ) × LCM ( p , q ) = a²b × a³b³

= a∧5b∧4 --------( 1 )

[∵ a∧m × b∧n = a∧m+n ]

pq = a²b³ × a³b

= a∧5 b∧4 ---------------( 2 )


from ( 1 ) and ( 2 ) , we conclude

HCF ( p , q ) × LCM ( p ,q ) = pq

I hope this helps you.