Find the smallest number that, when divided by 16, 18, and 21, leaves remainders of 3, 5, and 8 respectively.

Explanation

To solve this, subtract the respective remainders from the divisors to find a common number divisible by all three: (16 - 3) = 13, (18 - 5) = 13, and (21 - 8) = 13. The least common multiple (LCM) of 16, 18, and 21 is 1008. Adding the remainder 3 to the LCM gives 1008 + 3 = 1011, but since the remainders differ, we use the method of adjusting the number so that when divided by each divisor, the remainder matches. The correct smallest number satisfying these conditions is 995.