17. Given the set $S \subseteq\{1,2, \cdots, 12\},|S|=6$ ( $|S|$ represents the number of elements in the set $S$). If $a, b \in$ $S, a<b$, then $b$ is not a multiple of $a$. Then, the smallest element in the set $S$ is ( ).
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
17. C.

Obviously, $1 \notin S$, and among $\{2,4,8\}$, $\{3,6,12\}$, and $\{5,10\}$, at most one from each set can be in $S$.
Thus, $\{7,9,11\} \subset S \Rightarrow 3 \notin S$
$\Rightarrow 6$ or $12$ is in $S$ $\Rightarrow 2 \notin S$.
Upon verification, $\{4,5,6,7,9,11\}$ satisfies the requirements.