9. If two positive integers p and q are written as p=a2b3 and q=aba, b

1.	9. If two positive integers p and q are written as p=a2b3 and q=aba, b are primenumbers, then verify: LCM (p, q) x HCF (p, q)- pq. (CBSE 2017-2M)
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 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

9. If two positive integers p and q are written as p=a2b3 and q=aba, b are primenumbers, then verify: LCM (p, q) x HCF (p, q)- pq. (CBSE 2017-2M)

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 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