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      Question

      The total of two numbers is 130. If their LCM is 432 and

      HCF is 12, determine the smaller number.
      A 58 Correct Answer Incorrect Answer
      B 100 Correct Answer Incorrect Answer
      C 32 Correct Answer Incorrect Answer
      D 24 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the smaller number = ‘x’

      Greater number = (130 – x)

      Product of the numbers = product of their LCM and HCF

      Or, x(130 – x) = 12 × 432

      Or, 130x – x² = 5184

      Or, x² – 130x + 5184 = 0

      Or, x² – 72x – 58x + 5184 = 0

      Or, x(x – 72) – 58(x – 72) = 0

      Or, (x – 72)(x – 58) = 0

      Or, x = 72, 58

      When x = 72, (130 – x) = 58

      Therefore, x = 58

      So, the smaller number = 58

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