AMC 10 2022a 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 $17$? $\textbf{(A) } 1 \textbf{(B) } 3 \textbf{(C) } 5 \textbf{(D) } 7 \textbf{(E) } 9$