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    Question

    The total of two numbers is 130. If their LCM is 432 and

    HCF is 12, determine the smaller number.
    A 58 Correct Answer Incorrect Answer
    B 100 Correct Answer Incorrect Answer
    C 32 Correct Answer Incorrect Answer
    D 24 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the smaller number = ‘x’

    Greater number = (130 – x)

    Product of the numbers = product of their LCM and HCF

    Or, x(130 – x) = 12 × 432

    Or, 130x – x² = 5184

    Or, x² – 130x + 5184 = 0

    Or, x² – 72x – 58x + 5184 = 0

    Or, x(x – 72) – 58(x – 72) = 0

    Or, (x – 72)(x – 58) = 0

    Or, x = 72, 58

    When x = 72, (130 – x) = 58

    Therefore, x = 58

    So, the smaller number = 58

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