Question

if 2 positive integers p and q can be expressed as p = a{b}^{2} and q = {a}^{2}b where a and b are prime numbers, then find the LCM of a and b.

Answer 1

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.

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