List 3-digit numbers that leave remainder 4 when divided by 7, then check for remainder 3 when divided by 6.<br><br>
&bull; Numbers = 7k + 4. For 3-digit: k &ge; 14 (7&times;14+4 = 102)<br>
&bull; Try: 102 &divide; 6 = 17 r 0 &#10007;<br>
&bull; Try 109 &divide; 6 = 18 r 1 &#10007;<br>
&bull; Try 116 &divide; 6 = 19 r 2 &#10007;<br>
&bull; Try 123 &divide; 6 = 20 r 3 &#10003;<br>
&bull; 123 &divide; 7 = 17 r 4 &#10003;<br><br>
The smallest possible 3-digit number is 123.<br>
Final Answer: 123