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    Question

    The sum of two numbers is 144. Their LCM is 540 and HCF is

    15. What is the smaller number?
    A 54 Correct Answer Incorrect Answer
    B 45 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 = (144 – x)

    Product of the numbers = LCM × HCF

    Or, x(144 – x) = 15 × 540

    Or, 144x – x² = 8100

    Or, x² – 144x + 8100 = 0

    Or, x² – 90x – 54x + 8100 = 0

    Or, x(x – 90) – 54(x – 90) = 0

    Or, (x – 90)(x – 54) = 0

    So, smaller number = 54

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