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    Question

    The sum and difference of L.C.M and H.C.F of two numbers is

    312 and 208 respectively. If one of the numbers is 52, find the other number.
    A 260 Correct Answer Incorrect Answer
    B 144 Correct Answer Incorrect Answer
    C 239 Correct Answer Incorrect Answer
    D 126 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the L.C.M and the H.C.F of the two numbers be 'a' and 'b' respectively

    Then, (a + b) = 312

    And (a - b) = 208

    So, (a + b) + (a - b) = 312 + 208 = 520

    Or, a = 520 ÷ 2 = 260

    So, b = 312 - 260 = 52

    The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (260 × 52) ÷ 52 = 260

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