euler5

Problem

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

#include <stdio.h>

#define NUM 20

int main(int argc, const char *argv[])
{
    int num[NUM];
    int i, j;
    int result = 1;

    num[0] = 1;
    for (i = 1; i < NUM; i++) {
        num[i] = i;
        for (j = 1; j < i; j++) {
            if (!(num[i] % num[j]))
                num[i] /= num[j];
        }
    }

    for (i = 0; i < NUM; i++)
        result *= num[i];

    printf("result: %d\n", result);

    return 0;
}

很巧妙的办法，但怎么用数学的***明是正确的呢？