numbers, then verifyLCM (p, q) x HCF (p, q)pq

1.	numbers, then verifyLCM (p, q) x HCF (p, q)pq
Answer» take lcm and hcf which are common 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

Answer»

take lcm and hcf which are common

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

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