Question

2. If two positive integers P and q can be expressed as pra?b and q=ab? then find the LCM​

Answer 1

Answer:

Explanation:

p = a²b³

q = a³b

HCF ( p,q ) = a²b

[ ∵Product of the smallest power of 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

I hope this helps you.

: )

Answer 2

Answer:

Factors of p=a×b×b

Factors of q=a×a×a×b

Therefore, L.C.M. of p and q is =a×b×b×a×a

=a³ b²

Explanation:

hope it's helps you