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    Question

    LCM of two numbers is 5 times their HCF. The product of

    the numbers is 4500. What will be the maximum possible difference between the numbers?
    A 157 Correct Answer Incorrect Answer
    B 152 Correct Answer Incorrect Answer
    C 102 Correct Answer Incorrect Answer
    D 135 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 = 5 × x = 5x Or, x × 5x = 4500 Or, 5x² = 4500 Or, x² = 900 Or, x = √900 = 30 LCM of two numbers = 30 × 5 = 150 Let two numbers be ‘30a’ and ‘30b’, where ‘a’ and ‘b’ are co-prime numbers. So, 30ab = 150 Or, a × b = 5 So, when a = 1 and b = 5, then difference will be maximum Desired difference = 30 × 5 – 30 × 1 = 120

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