We multiply the first ratio by 4 on both sides, and the second ratio by 3 to get the same number for 8 th graders, in order that we can put the two ratios together: $$ \begin{aligned} \&11: 6=11(4): 6(4)=44: 24 \textbackslash\textbackslash{} \&8: 13=8(3): 13(3)=24: 39 \end{aligned} $$ Therefore, the ratio of 8th graders to 7th graders to 6th graders is $44: 24: 39$. Since the ratio is in lowest terms, the smallest number of students participating in the project is $$ 44+24+39=\text { (C) } 107 $$ 
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 $11: 6$, and the the ratio of $8^{\text {th }}$-graders to $7^{\text {th }}$ graders is $8: 13$. What is the smallest number of students that could be participating in the project? (2013 AMC 8, Question 16) 
Options:
A. $$44$$ 
B. $$84$$ 
C. $$107$$ 
D. $$150$$ 
E. $$214$$ 