Problem 10. The correct answer is (D).

The possible triples $(a, b, c)$ are: $\quad(1,2,4), \quad(1,2,6), \quad(1,2,12), \quad(1,3,6), \quad(1,3,12), \quad(1,4,12), \quad(1,6,12)$, $(2,4,12), \quad(2,6,12), \quad(3,6,12)$. In total, there are 10.
10. How many triples of distinct natural numbers $(a, b, c)$ are there such that the number $a$ is a divisor of $b$, the number $b$ is a divisor of $c$, and the number $c$ is a divisor of 12?
(A) 6
$\begin{array}{ll}\text { (B) } 7 & \text { (C) } 8\end{array}$
(D) 10
(E) 9