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      Question

      The sum of two numbers is 144. Their LCM is 540 and HCF is

      15. What is the smaller number?
      A 54 Correct Answer Incorrect Answer
      B 45 Correct Answer Incorrect Answer
      C 32 Correct Answer Incorrect Answer
      D 24 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the smaller number = тАШxтАЩ

      Greater number = (144 тАУ x)

      Product of the numbers = LCM ├Ч HCF

      Or, x(144 тАУ x) = 15 ├Ч 540

      Or, 144x тАУ x┬▓ = 8100

      Or, x┬▓ тАУ 144x + 8100 = 0

      Or, x┬▓ тАУ 90x тАУ 54x + 8100 = 0

      Or, x(x тАУ 90) тАУ 54(x тАУ 90) = 0

      Or, (x тАУ 90)(x тАУ 54) = 0

      So, smaller number = 54

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