The number is 1 more than a common multiple of 2, 3, and 4.<br><br>
&bull; LCM of 2, 3, and 4 = 12<br>
&bull; The number = 12k + 1<br>
&bull; For the smallest with positive quotient for &divide;4: k = 1<br>
&bull; 12 &times; 1 + 1 = 13<br>
&bull; Check: 13 &divide; 2 = 6 r 1 &#10003;, 13 &divide; 3 = 4 r 1 &#10003;, 13 &divide; 4 = 3 r 1 &#10003;<br><br>
The smallest possible number is 13.<br>
Final Answer: 13