AMC 8 2018 Problem 10

The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4? $\textbf{(A) }\frac{3}{7} \textbf{(B) }\frac{7}{12} \textbf{(C) }\frac{12}{7} \textbf{(D) }\frac{7}{4} \textbf{(E) }\frac{7}{3}$