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? Choose one:
A) 1108
B) 1683
C) 2007
D) 3363
E) 3567
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.   Answer: Option 1683
<result>B</result>
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?