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

  1. The LCM of two numbers is 8919, and their sum is 1000. The two numbers are:

    2. A.
    993 and 7
    B.
    989 and 11
    C.
    991 and 9
    D.
    987 and 13

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    Answer : Option C

    Explanation :

    Let the two numbers be x and (1000 - x)

    ∴ x * (1000 - x) = 8919
         1000x - x2 = 8919
         -x2 + 1000x -8919 = 0
         -x2 + ( 991 + 9)x - 8919 = 0
         -x2 + 991x +9x - 8919 = 0
         -x(x - 991) + 9(x - 991) = 0
         (x - 991) (-x + 9) = 0

    ∴ (x - 991) = 0
         X = 991, and
         (-x + 9) = 0
         -x = -9
         X = 9
    So, the required numbers are 991 and 9.

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