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    Question

    The square of sum of two numbers is 25,600 and the sum

    of squares of the same two numbers is 13,000. If their H.C.F. is 10, then find their L.C.M.
    A 420 Correct Answer Incorrect Answer
    B 560 Correct Answer Incorrect Answer
    C 630 Correct Answer Incorrect Answer
    D 700 Correct Answer Incorrect Answer

    Solution

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

    We have, (a + b) ² = 25600
    And, a² + b² = 13000

    (a + b) ² = a² + b² + 2ab = 13000 + 2ab

    Or, 2ab = 25600 - 13000 = 12600

    So, ab = 12600/2 = 6300

    Therefore, L.C.M = 6300 / 10 = 630

    Hence, option C.

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