Problem 5 (C++)

#include <iostream>
using namespace ::std;
int main()
{
        int primes[] = {2,3,5,7,11,13,17,19,23};//up to 22 numbers
        int n = 1;
        int temp;
        int nums = 20;

        for(int i=0; primes[i] <= nums; i++)
        {
                temp = 1;
                while(temp < nums)
                {
                        if(temp * primes[i] <= nums)
                        {
                                temp *= primes[i];
                        }
                        else {break;}
                }
                n *= temp;
        }
        cout << n;
        cin >> n;//pause
        return 0;
}