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      Question

      The HCF of two numbers is 21 and their LCM is 693. If

      one of the numbers is 63, find the other number and verify that it is a multiple of the HCF.
      A 335 Correct Answer Incorrect Answer
      B 231 Correct Answer Incorrect Answer
      C 169 Correct Answer Incorrect Answer
      D 273 Correct Answer Incorrect Answer

      Solution

      For two numbers a and b: a Γ— b = HCF Γ— LCM Let other number = x. 63 Γ— x = 21 Γ— 693 Compute RHS: 21Γ—693 = 21Γ—(700 βˆ’ 7) = 14,700 βˆ’ 147 = 14,553 So x = 14,553 / 63 63Γ—200 = 12,600 Remaining: 1,953 63Γ—30 = 1,890 Remaining: 63 So x = 200 + 30 + 1 = 231 Check: 231 Γ· 21 = 11, So 231 is a multiple of the HCF.

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