The smallest and largest three digit numbers, respectively, are 100 and 999.

We divide each by 3

   33         333
3)100       3)999
   9          9
   10          9 
    9          9 
    1           9
                9
                0

100 leaves a remainder, so we increase 33 to the next integer, 34 and multiply
that by 3 and get 102, so that's the initial three digit number divisible by 3.
Since 999 did not leave a remainder, it's divisible by 3, so it's the final
value of the counting variable.

Answers: 102 and 999
  
Edwin