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      Question

      The sum and difference of the Least Common Multiple

      (L.C.M.) and Highest Common Factor (H.C.F.) of two numbers are 216 and 184, respectively. If one of the numbers is 25, find the other number.
      A 144 Correct Answer Incorrect Answer
      B 128 Correct Answer Incorrect Answer
      C 108 Correct Answer Incorrect Answer
      D 136 Correct Answer Incorrect Answer

      Solution

      Let the L.C.M and the H.C.F of the two numbers be 'a' and 'b' respectively Then, (a + b) = 216 And (a - b) = 184 So, (a + b) + (a - b) = 216 +184 Or, a = 400 ├╖ 2 = 200 So, b = 216 - 200 = 16 The product of two numbers is equal to the product of their L.C.M and H.C.F So, required number = (200 X 16) ├╖ 25 = 128

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