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      Question

      The square of sum of two numbers is 4,096 and the sum of

      squares of the same two numbers is 2,176. If their H.C.F. is 8, then find their L.C.M.
      A 96 Correct Answer Incorrect Answer
      B 160 Correct Answer Incorrect Answer
      C 120 Correct Answer Incorrect Answer
      D 144 Correct Answer Incorrect Answer

      Solution

      Let the two numbers be 'a' and 'b'

      We have, (a + b)² = 4096
      And, a² + b² = 2176

      (a + b) ² = a² + b² + 2ab = 2176 + 2ab

      Or, 2ab = 4096 - 2176 = 1920

      So, ab = 1920/2 = 960

      Since product of two numbers = L.C.M × H.C.F.

      Therefore, L.C.M = 960 / 8 = 120

      Hence, option C.

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