Question

If two positive integers P and Q are written as P=a^2 b^3 ; a, b are prime numbers, then verify lcm (p, q) *hcf (p, q) = pq

Answer 1

Answer:

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.

: )