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    Question

    LCM of two numbers is 18 times their HCF. The product of

    the numbers is 64800. What will be the maximum possible difference between the numbers?
    A 1578 Correct Answer Incorrect Answer
    B 1552 Correct Answer Incorrect Answer
    C 1020 Correct Answer Incorrect Answer
    D 1535 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let HCF of two numbers be ‘x’ So, LCM of two numbers = 18 × x = 18x Or, x × 18x = 64800 Or, 18x² = 64800 Or, x² = 3600 Or, x = √3600 = 60 LCM of two numbers = 60 × 18 = 1080 Let two numbers be ‘60a’ and ‘60b’, where ‘a’ and ‘b’ are co-prime numbers. So, 60ab = 1080 Or, a × b = 18 So, when a = 1 and b = 18, then difference will be maximum Desired difference = 60 × 18 – 60 × 1 = 1020

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