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If two positive integers A and …

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If two positive integers A and B are written as A=ab cube and B=a cube b square, a, being prime number then HCF (A,B) is

    • Posted by Khushi Sid 5 years, 2 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 5 years ago

    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

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