LCM program in C++

#include <iostream>
using std::cout;
using std::cin;

int main()
{

    int num1 = 0;
    int num2 = 0;

    cout << "Please enter two numbers (remember to put 
a space between them):\n";

    cin >> num1 >> num2;

    const int num_limit = num1 * num2;

    for (int i = 1; i <= num_limit; i++)
    {
        int product = num1 * i;
        int product2 = num2 * i;

        // test for when multiples are equal
        if (product == product2)
        {
        cout << "The LCM of " << num1 << " and " << 
num2 << " is: "; 
        }

     }
}

I'm trying to get the LCM from two integers which the user enters. The if statement within the for loop isn't doing what I intended it to do, as nothing prints when product and product2 are equal. What is the solution to this little problem?

Try this out

//#include "stdafx.h"
#include <iostream>
#include <conio.h>
using std::cout;
using std::cin;

int main()
{

    int num1 = 0;
    int num2 = 0;

    cout << "Please enter two numbers (remember to put a space between them):\n";

    cin >> num1 >> num2;

    int num_limit = num1 * num2,LCM;
    for (int i = 1; i <= num_limit; i++)
    {
        LCM = num1 * i;

        // test for when multiples are equal
        if (LCM%num2==0) break;
    }
    cout << "The LCM of " << num1 << " and " << num2 << " is: " << LCM;
    _getch();// replace with getch(); if didn't work
}