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Discussion :: Problems on H.C.F and L.C.M

  1. The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:

    2. A.

    1
    B.

    2
    C.

    3
    D.

    4

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    Answer : Option B

    Explanation :

    Let the numbers 13a and 13b.

     

    Then, 13a x 13b = 2028

     

     ab = 12.

     

    Now, the co-primes with product 12 are (1, 12) and (3, 4).

     

    [Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]

     

    So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).

     

    Clearly, there are 2 such pairs.

     

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