VTMO 2026 - Grade 6 - Semifinal - SET 10 - Self-study Question 2

Define $n!$ (n factorial) as the product of all natural numbers from 1 to $n$. For example, $2021!=1\times2\times3\times\cdots\times2021$. Find the smallest $n$ for which $n!$ is divisible by both 2020 and 2021.