Am I right in this logic?

See more:

C++

I had a problem:
Given a number X, find the smallest number that will be divisible by all numbers from 1 till X.

The logic I implemented is :
1) Create a array of X elements with same value. a[0]=1,a[1]=2 ...etc.
2) First loop from a[1] to a[X-1] (int 0<=i<x)>
3) Select an element of array for each iteration a[i](a[1] then a[2] then a[3]...)
4) Second loop inside this loop from a (i+1<= j < X)
5) Divide each element of array(a[j]) in this loop with element selected in first loop a[i] if a[j]%a[i]==0 and a[i]!=1

I am getting answers right I checked upto num 15.
Its just that logic I found on net was quite different. I am also adding code so that it will be more clear (my logic explanation is quite confusing i think :P). If any one have a better logic please suggest.

#include <iostream>
#include <string>
#include <cassert>
using namespace std;

int smallest_div(int num)
{
    int *array = new int[num];
    int result(1);
    for (int i(0);i<num;i++)>
     array[i]=i+1;
    for(int i=1;i<num;i++)>
    {
        for(int j=i+1;j<num;j++)>
        {
            if(array[j]%array[i]==0 && array[j]!=1 && array[i]!=1)
            {
                array[j]=array[j]/array[i];
            }

        }
    
    }

    cout <<"\nFinal Array:"<<endl;
    for (int i(0);i<num;i++)>
    {
            result*=array[i];
            cout << " "<<array[i];
    }
    delete[] array;
    array=0;

    return result;

}

 int main(void)
 {
   int n,r;
   cout << "Enter the num. :";
   cin >> n;
   r=smallest_div(n);
   cout <<"\nSmallest divisible num = "<<r;

 }

*Ignore > sign after every for loop