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    Question

    Two numbers have a sum of 112. If their LCM is 420 and HCF

    is 6, determine the smaller number.
    A 54 Correct Answer Incorrect Answer
    B 45 Correct Answer Incorrect Answer
    C 32 Correct Answer Incorrect Answer
    D 28 Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the smaller number = тАШxтАЩ

    Greater number = (112 тАУ x)

    Product of numbers = LCM ├Ч HCF

    Or, x(112 тАУ x) = 6 ├Ч 420

    Or, 112x тАУ x┬▓ = 2520

    Or, x┬▓ тАУ 112x + 2520 = 0

    Or, x┬▓ тАУ 84x тАУ 28x + 2520 = 0

    Or, x(x тАУ 84) тАУ 28(x тАУ 84) = 0

    Or, (x тАУ 84)(x тАУ 28) = 0

    So, smaller number = 28

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