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    Question

    The square of sum of two numbers is 4,096 and the sum of

    squares of the same two numbers is 2,176. If their H.C.F. is 8, then find their L.C.M.
    A 96 Correct Answer Incorrect Answer
    B 160 Correct Answer Incorrect Answer
    C 120 Correct Answer Incorrect Answer
    D 144 Correct Answer Incorrect Answer

    Solution

    Let the two numbers be 'a' and 'b'

    We have, (a + b)² = 4096
    And, a² + b² = 2176

    (a + b) ² = a² + b² + 2ab = 2176 + 2ab

    Or, 2ab = 4096 - 2176 = 1920

    So, ab = 1920/2 = 960

    Since product of two numbers = L.C.M × H.C.F.

    Therefore, L.C.M = 960 / 8 = 120

    Hence, option C.

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