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 $\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots +\frac{1}{13}=\frac{h}{L_{13}}$. What is the remainder when $h$ is divided by $13$?