Question numbers 7 to 12 carry 2 marks each.If two positive integers p

1.	Question numbers 7 to 12 carry 2 marks each.If two positive integers p and q are written as p a bnumbers, then verify:and q ab; a, b are prime7LCM (p, q) x HCF (p, q)-pq
Answer» p = a²b³ q = a³b HCF ( p,q ) = a²b [∵Product of the smallest powerof each common prime factors in the numbers ] LCM ( p , q ) = a³b³[∵ Product of the greatest power of eachprime 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

Question numbers 7 to 12 carry 2 marks each.If two positive integers p and q are written as p a bnumbers, then verify:and q ab; a, b are prime7LCM (p, q) x HCF (p, q)-pq

Answer»

p = a²b³

q = a³b

HCF ( p,q ) = a²b

[∵Product of the smallest powerof each common prime factors in the numbers ]

LCM ( p , q ) = a³b³[∵ Product of the greatest power of eachprime 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