Question

If two +ve integers p and q are written as p= a²b³ and q= a³b ; a,b are prime numbers ,then verify LCM(p,q)×HCF(p,q)= pq

Answer 1

hcf of p and q= a2b
lcm= a3b3

verification,
hcf*lcm=product of two numbers
a2b*a3b3=a2b3*a3b
a5b4=a5b4
(verified)

Answer 2

Hi ,

It is given that

p , q are two positive Integers ,

and a , b are prime .

p = a² b³ -------( 1 )

q = a³ b ---------( 2 )

HCF ( p , q ) = a²b ------( 3 )

[ since , product of the smallest power of

each common prime factors of the numbers ]

LCM( p , q ) = a³ b³ ----( 4 )

[ product of the greatest power of each

prime factors of the numbers ]

verification:
__________

LCM × HCF = (4 ) × ( 3 )

= a³ b³ × a² b

= a^5 b⁴ ----( 5 )

p × q = a²b³ × a³ b

= a^5 b⁴ ----- ( 6 )

Therefore

LCM × HCF = p × q

I hope this helps you.

:)