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      Question

      The sum and difference of L.C.M and H.C.F of two numbers is

      312 and 208 respectively. If one of the numbers is 52, find the other number.
      A 260 Correct Answer Incorrect Answer
      B 144 Correct Answer Incorrect Answer
      C 239 Correct Answer Incorrect Answer
      D 126 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the L.C.M and the H.C.F of the two numbers be 'a' and 'b' respectively

      Then, (a + b) = 312

      And (a - b) = 208

      So, (a + b) + (a - b) = 312 + 208 = 520

      Or, a = 520 ├╖ 2 = 260

      So, b = 312 - 260 = 52

      The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (260 ├Ч 52) ├╖ 52 = 260

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