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      Question

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

      numbers are 486 and 342. If one of the numbers is 18, find the other number.
      A 1656 Correct Answer Incorrect Answer
      B 1744 Correct Answer Incorrect Answer
      C 1639 Correct Answer Incorrect Answer
      D 1826 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) = 486

      And (a - b) = 342

      So, (a + b) + (a - b) = 486 + 342 = 828

      Or, a = 828 ÷ 2 = 414

      So, b = 486 - 414 = 72

      The product of two numbers is equal to the product of their L.C.M and H.C.FSo, required number = (414 × 72) ÷ 18 = 1656

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