That least positive multiple

We want to find the least $k \in \mathbb{N}$ such that $2017k \equiv 2018 \pmod{10^4}$ . But it is equivalent to $2017(k-1) \equiv 1 \pmod{10^4}$ , so $k-1$ is the multiplicative inverse of $2017$ modulo $10^4$ , which is $4353$ . Therefore, $k=4354$ and the answer is $2017 \cdot 4354 = 8782018$ .