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    Question

    The square of sum of two numbers is 36,864 and the sum

    of squares of the same two numbers is 21,024. If their H.C.F. is 12, then find their L.C.M. 
    A 660 Correct Answer Incorrect Answer
    B 540 Correct Answer Incorrect Answer
    C 600 Correct Answer Incorrect Answer
    D 720 Correct Answer Incorrect Answer

    Solution

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

    We have, (a + b) ² = 36864
    And, a² + b² = 21024

    (a + b) ² = a² + b² + 2ab = 21024 + 2ab

    Or, 2ab = 36864 – 21024 = 15840

    So, ab = 15840/2 = 7920

    Therefore, L.C.M = 7920 / 12 = 660

    Hence, option A.

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