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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 β€˜x’ So, LCM of two numbers = 8 Γ— x = 8x Or, x Γ— 8x = 10240 Or, 8xΒ² = 10240 Or, xΒ² = 1280 Or, x = √1280 = 35.78 (Approx 36) LCM of two numbers = 36 Γ— 8 = 288 Let two numbers be β€˜36a’ and β€˜36b’, where β€˜a’ and β€˜b’ are co-prime numbers. So, 36ab = 288 Or, a Γ— b = 8 So, when a = 1 and b = 8, then difference will be maximum Desired difference = 36 Γ— 8 – 36 Γ— 1 = 252

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