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      Question

      Two numbers have a sum of their LCM and HCF equal to

      464, and their LCM is 28 times their HCF. One of the numbers is 64. Find the difference between the two numbers.
      A 54 Correct Answer Incorrect Answer
      B 60 Correct Answer Incorrect Answer
      C 48 Correct Answer Incorrect Answer
      D 72 Correct Answer Incorrect Answer

      Solution

      Let the HCF of the numbers = x LCM of the numbers = 28x According to the question, 28x + x = 464 Or, 29x = 464 Or, x = 16 HCF of the numbers = 16 LCM of the numbers = 28 × 16 = 448 As we know, Product of two numbers = product of their LCM and HCF Or, 64 × second number = 16 × 448 Or, second number = {(16 × 448)/64} = 112 Required difference between the numbers = 112 – 64 = 48

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