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    Question

    The Least Common Multiple (LCM) of two numbers is 15

    times their Highest Common Factor (HCF). The product of these two numbers is 15,360. What is the maximum possible difference between these numbers?
    A 448 Correct Answer Incorrect Answer
    B 512 Correct Answer Incorrect Answer
    C 416 Correct Answer Incorrect Answer
    D 544 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let HCF of two numbers be тАШxтАЩ So, LCM of two numbers = 15 ├Ч x = 15x Or, x ├Ч 15x = 15360 Or, 15x2┬а= 15360 Or, x2┬а= 1024 Or, x = 32 LCM of two numbers = 32 ├Ч 15 = 480 Let two number be тАШ32aтАЩ and тАШ32bтАЩ, where тАШaтАЩ and тАШbтАЩ are co-prime numbers. So, 32ab = 480 Or, a ├Ч b = 15 So, when a = 1 and b = 15, then difference will be maximum Desired difference = 32 ├Ч 15 тАУ 32 ├Ч 1 = 448

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