What is the smallest result that can be obtained from the following process?

Choose three different numbers from the set $\{3,5,7,11,13,17\}$.
Add two of these numbers.
Multiply their sum by the third number.
$\text{(A)}\ 15 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 50 \qquad \text{(E)}\ 56$
Since we want the smallest possible result, and we are only adding and multiplying positive numbers over $1$, we can "prune" the set to the three smallest numbers $\{3,5,7\}$.  Using bigger numbers will create bigger sums and bigger products.
From there, compute the $3$ ways you can do the two operations:
$(3+5)7 = 8\cdot 7 = 56$
$(3 + 7)5 = 10\cdot 5 = 50$
$(7+5)3 = 12\cdot 3 = 36$
The smallest number is 36, giving an answer of $\boxed{C}$