What is the least number which when divided by 5, 6, 7, 8 gives the remainder 3 but is divisible by 9?

The number must be 3 more than a multiple of LCM(5,6,7,8) = 840. So it's of form 840k + 3, and also divisible by 9. Testing: k=1 gives 843 (sum=15, not divisible by 9). k=2 gives 1683 (sum=18, divisible by 9). k=3 gives 2523 (sum=12, not divisible by 9). The LCM condition requires the remainder 3 for each divisor, so 1683 is the least such number. Option A (1793) gives wrong remainders.