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    Question

    LCM of two numbers is 10 times their HCF. The product of

    the numbers is 18000. What will be the maximum possible difference between the numbers?
    A 378 Correct Answer Incorrect Answer
    B 375 Correct Answer Incorrect Answer
    C 356 Correct Answer Incorrect Answer
    D 335 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let HCF of two numbers be тАШxтАЩ So, LCM of two numbers = 10 ├Ч x = 10x Or, x ├Ч 10x = 18000 Or, 10x┬▓ = 18000 Or, x┬▓ = 1800 Or, x = тИЪ1800 = 42.43 (Approx 42) LCM of two numbers = 42 ├Ч 10 = 420 Let two numbers be тАШ42aтАЩ and тАШ42bтАЩ, where тАШaтАЩ and тАШbтАЩ are co-prime numbers. So, 42ab = 420 Or, a ├Ч b = 10 So, when a = 1 and b = 10, then difference will be maximum Desired difference = 42 ├Ч 10 тАУ 42 ├Ч 1 = 378

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