AMC 8 2013 Problem 16

A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^\text{th}$-graders to $6^\text{th}$-graders is $5:3$, and the the ratio of $8^\text{th}$-graders to $7^\text{th}$-graders is $8:5$. What is the smallest number of students that could be participating in the project? $\textbf{(A)}\ 16 \textbf{(B)}\ 40 \textbf{(C)}\ 55 \textbf{(D)}\ 79 \textbf{(E)}\ 89$