2022 AMC 10A Problem 19

Define L_n as the least common multiple of all the integers from 1 to n inclusive. There is a unique integer h such that \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{17}=\frac{h}{L_{17}} What is the remainder when h is divided by 17?

\textbf{(A) } 1 \qquad \textbf{(B) } 3 \qquad \textbf{(C) } 5 \qquad \textbf{(D) } 7 \qquad \textbf{(E) } 9

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.