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      Question

      Two numbers have a sum of 112. If their LCM is 420 and HCF

      is 6, determine the smaller number.
      A 54 Correct Answer Incorrect Answer
      B 45 Correct Answer Incorrect Answer
      C 32 Correct Answer Incorrect Answer
      D 28 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the smaller number = ‘x’

      Greater number = (112 – x)

      Product of numbers = LCM × HCF

      Or, x(112 – x) = 6 × 420

      Or, 112x – x² = 2520

      Or, x² – 112x + 2520 = 0

      Or, x² – 84x – 28x + 2520 = 0

      Or, x(x – 84) – 28(x – 84) = 0

      Or, (x – 84)(x – 28) = 0

      So, smaller number = 28

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