A 3-digit number, when divided by 3, has a remainder of 2. When the same number, when divided by 6, has a remainder of 5. What is the smallest possible number?
Lowest common multiple of 3 and 6 = 6

Since it is a 3-digit number, to be the smallest possible number, it has to be as close to 100 as possible.

100 ÷ 6 = 16 r 4

Quotient to be multiplied by 6 to produce the smallest 3-digit number 
= 16 + 1
= 17

Smallest 3-digit number that is divisible by 6
= 17 x 6
= 102

Since the number has a remainder of 2 when divided by 3 and it has to be the smallest possible 3-digit number, we can find the difference between the divisor and the reminder.

Number to be subtracted from the smallest 3-digit number that is divisible by 6
= 3 - 2
= 1

Then we use the smallest 3-digit number that is divisible by 6 and subtract it by the difference to find the answer.

Smallest 3-digit number so that there is a remainder of 2 when divided by 3 and a remainder of 5 when divided by 6
= 102 - 1
= 101

Answer(s): 101