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Q: Find the least positive number; which when divided by 5, 6, 8, 9 and 12 gives 1 as a remainder in each case and is completely divisible by 13.
  • A. 3640
  • B. 3614
  • C. 3601
  • D. 3627
Correct Answer: Option C - L.C.M of 5, 6, 8, 9 and 12 is = 360 ∴ Required number = 360 K + 1 On putting K = 10, Number is completely divisible by 13. ∴ Required number = 360 × 10 + 1 = 3600 + 1 = 3601
C. L.C.M of 5, 6, 8, 9 and 12 is = 360 ∴ Required number = 360 K + 1 On putting K = 10, Number is completely divisible by 13. ∴ Required number = 360 × 10 + 1 = 3600 + 1 = 3601

Explanations:

L.C.M of 5, 6, 8, 9 and 12 is = 360 ∴ Required number = 360 K + 1 On putting K = 10, Number is completely divisible by 13. ∴ Required number = 360 × 10 + 1 = 3600 + 1 = 3601