解题思路：

动态规划

需要熟练掌握最小公倍数和最大公约数的计算

import java.util.*;

public class Main {
    public static void main(String[] args) {
        int[] dp = new int[2022];
        dp[1] = 0;
        for (int i = 2; i <= 2021; i++) {
            dp[i] = Integer.MAX_VALUE;
        }

        for (int i = 1; i <= 2020; i++) {
            for (int j = i + 1; j <= 2021 && (j - i <= 21); j++) {
                dp[j] = Math.min(dp[i] + le(i, j), dp[j]);
            }
        }
        System.out.print(dp[2021]);
    }

    public static int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    public static int le(int a, int b) {
        return a * b / gcd(a, b);
    }
}