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      Question

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

      LCM and HCF is 403 and if both the number are smaller than their LCM. Find both the numbers?
      A 82,126 Correct Answer Incorrect Answer
      B 74,130 Correct Answer Incorrect Answer
      C 93, 124 Correct Answer Incorrect Answer
      D 92,148 Correct Answer Incorrect Answer

      Solution

      HCF = H, LCM = 12H Sum → H + 12 H = 403 H = 31 HCF = 31        LCM = 12 × 31 H = 31 Let No’s 31x      31y LCM ⇒ 31xy = 12 × 31 ⇒ xy = 12 If (1, 12) ⇒ 1 × 31 = 31, 31 × 12 = 372 → not less than LCM If (3, 4) ⇒ 3 × 31 , 4 × 31 = 93, 124 

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