java中的彩票游戏

Question

我在为彩票游戏编写java程序时遇到问题我编写的程序可以正常工作，但是我无法让总和部分正常工作。我需要它添加每一个数字，例如，如果结果打印234,456,345我需要添加2 + 3 + 4 + 4 + 5 + 6 + 3 + 4 + 5然后返回总和但我得到的是234+ 456 + 345任何帮助都会很好。

import java.util.Scanner;
public class LotteryDraw {
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int game;
        int times;
        int randNum; 
        int lotNum;
        int sum = 0;
        System.out.println("Which lottery game do you want to play!");
        System.out.println("Enter 3 for Pick 3");
        System.out.println("Enter 4 for Pick 4");
        System.out.println("Enter 5 for Pick 5");
        game = input.nextInt();

        System.out.print("How many games would you like to play? ");
        times = input.nextInt();
        System.out.println("Thank you! The numbers selected were: ");
        for(int i = 0; i < times; i++) {
            lotNum = 0;
            for(int j = 0; j < game; j++)
            {
                randNum = (new java.util.Random()).nextInt(10);
                lotNum = (lotNum * 10) + randNum;
                System.out.print(randNum);
            }
            System.out.println();
            sum += lotNum;   
        }
        System.out.println("Sum of the numbers of all games: " + sum);
    }
}