LCM program in java giving wrong output

My java program for finding the LCM of two numbers is giving wrong output for (13, 12). Please check what is the error. I think the error is with the loop I cannot figure out what to do next help me please.

import java.util.*;
public class Bonjour{
    public static void main(String args[]){
        Scanner scan = new Scanner(System.in);
        System.out.println("Enter 2 numbers: ");
        int num1 = scan.nextInt();
        int num2 = scan.nextInt();
        if(num1 % num2 == 0)
        {
            System.out.println("The LCM = "+num1);
        }
        else if(num2 % num1 == 0)
        {
            System.out.println("The LCM = "+num2);
        }
        else if(num2 % num1 != 0) // 2, 3 = 6;
        {
            for(int i = 1;i <= 100;i++){
                if(((num1 * i) % num2) == 0){
                    System.out.println("The LCM = "+(num1 * i));
                    break;
                   }
            }
         }
         else{
             System.out.println("The LCM = "+(num1*num2));
         }
         scan.close();
        }
     }

The output of the program when I input(12, 13) is blank. But it is working for other inputs. Sample output for '12' and '13'.

Enter 2 numbers:
12
13
//No output??

Sample output for '3' and '2':

Enter 2 numbers:
3
2
The LCM = 6