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    Question

    LCM of two numbers is 8 times their HCF. The product of

    the numbers is 10240. What will be the maximum possible difference between the numbers?
    A 178 Correct Answer Incorrect Answer
    B 252 Correct Answer Incorrect Answer
    C 256 Correct Answer Incorrect Answer
    D 235 Correct Answer Incorrect Answer

    Solution

    ATQ, Let HCF of two numbers be тАШxтАЩ So, LCM of two numbers = 8 ├Ч x = 8x Or, x ├Ч 8x = 10240 Or, 8x┬▓ = 10240 Or, x┬▓ = 1280 Or, x = тИЪ1280 = 35.78 (Approx 36) LCM of two numbers = 36 ├Ч 8 = 288 Let two numbers be тАШ36aтАЩ and тАШ36bтАЩ, where тАШaтАЩ and тАШbтАЩ are co-prime numbers. So, 36ab = 288 Or, a ├Ч b = 8 So, when a = 1 and b = 8, then difference will be maximum Desired difference = 36 ├Ч 8 тАУ 36 ├Ч 1 = 252

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