What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

A. 1108

B. 1683

C. 2007

D. 3363

Answer: Option B

Solution(By Examveda Team)

LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9
If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9
If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9
Hence, 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder