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      Question

      The square of sum of two numbers is 25,600 and the sum

      of squares of the same two numbers is 13,000. If their H.C.F. is 10, then find their L.C.M.
      A 420 Correct Answer Incorrect Answer
      B 560 Correct Answer Incorrect Answer
      C 630 Correct Answer Incorrect Answer
      D 700 Correct Answer Incorrect Answer

      Solution

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

      We have, (a + b) ² = 25600
      And, a² + b² = 13000

      (a + b) ² = a² + b² + 2ab = 13000 + 2ab

      Or, 2ab = 25600 - 13000 = 12600

      So, ab = 12600/2 = 6300

      Therefore, L.C.M = 6300 / 10 = 630

      Hence, option C.

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