Multiple choice

Three numbers are in the ratio of (2:3:5) and their LCM is (90). Find their HCF.

  1. $9$
  2. $1$
  3. $6$
  4. $3$
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D Correct answer
Explanation

Numbers are in ratio 2:3:5, so let them be 2k, 3k, 5k. Their LCM = 90. 2k, 3k, 5k have LCM = 30k (since 2, 3, 5 are coprime). So 30k = 90, giving k = 3. The numbers are 6, 9, 15. Their HCF = 3. Alternatively: LCM = k × LCM(2,3,5) = k × 30 = 90, so k = 3. HCF = k × HCF(2,3,5) = 3 × 1 = 3.

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