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      Question

      LCM of two numbers is 12 times their HCF. The product of

      the numbers is 25920. What will be the maximum possible difference between the numbers?
      A 578 Correct Answer Incorrect Answer
      B 552 Correct Answer Incorrect Answer
      C 506 Correct Answer Incorrect Answer
      D 535 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 = 12 × x = 12x Or, x × 12x = 25920 Or, 12x² = 25920 Or, x² = 2160 Or, x = √2160 = 46.48 (Approx 46) LCM of two numbers = 46 × 12 = 552 Let two numbers be ‘46a’ and ‘46b’, where ‘a’ and ‘b’ are co-prime numbers. So, 46ab = 552 Or, a × b = 12 So, when a = 1 and b = 12, then difference will be maximum Desired difference = 46 × 12 – 46 × 1 = 506

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