The Problem

You are given an integer $$$K$$$ greater than or equal to $$$2$$$. Find the minimum positive integer $$$N$$$ such that $$$N!$$$ is a multiple of $$$K$$$.

Here, $$$N!$$$ denotes the factorial of $$$N$$$. Under the Constraints of this problem, we can prove that such an $$$N$$$ always exists.

Constraint: $$$2 \leq K \leq 10 ^12$$$

The submission

Here are the interactions. ChatGPT spoke Chinese to me (which I didn't figure out how to configure it), so I'd provide some translations here.

Human: (The problem statement with hint to use long long)

ChatGPT: We can use code to implement the above algorithm.

Commment: ChatGPT wrote a bruteforce algorithm, which is reasonable.