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Q: Find the smallest 3 digit number which when added to 5 is exactly divisible by 12, 14 and 18.
  • A. 240
  • B. 225
  • C. 247
  • D. 245
Correct Answer: Option C - ∵The smallest number which is completely divisible by 12, 14 and 18 = The LCM of 12, 14, 18. 12 = 2 × 2 × 3 14 = 2 × 7 18 = 2 × 3 × 3 LCM = 2×2×3×3×7 = 252 Hence, the required number · 252 – 5 = 247
C. ∵The smallest number which is completely divisible by 12, 14 and 18 = The LCM of 12, 14, 18. 12 = 2 × 2 × 3 14 = 2 × 7 18 = 2 × 3 × 3 LCM = 2×2×3×3×7 = 252 Hence, the required number · 252 – 5 = 247

Explanations:

∵The smallest number which is completely divisible by 12, 14 and 18 = The LCM of 12, 14, 18. 12 = 2 × 2 × 3 14 = 2 × 7 18 = 2 × 3 × 3 LCM = 2×2×3×3×7 = 252 Hence, the required number · 252 – 5 = 247