Project Euler Problem #5 - Smallest Multiple (in Java)

public class Problem_5_Smallest_Multiple {

    /* 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? */

    public static void main(String[] args) {
        System.out.println(findSmallestMultiple(10)); // 2520
        System.out.println(findSmallestMultiple(20));
    }
    
    /* returns smallest multiple that is evenly divisible by all numbers from 1 - n
     * returns -1 if multiple does not exist
     * works up to n = 20 (long reaches maximum value for values > 20) */
    public static long findSmallestMultiple(int n) {
        for (long i = n; i <= factorial(n); i += n) {
            if (isMultiple(i, n)) return i;
        }
        return -1;
    }
    
    /* checks every number between 1 and n to see if x is a multiple of every number
     * returns true if x is found to be a multiple of every number, and false if x is
     * found to not be a multiple of any number */ 
    public static boolean isMultiple(long x, int n) {
        for (int i = 1; i < n; i++) {
            if (x % i != 0) return false;
        }
        return true;
    }
    
    /* returns the n factorial, or -1 if it does not exist; works up to 20 */
    public static long factorial (long n) {
        if (n > 1) return n * factorial(n - 1);
        else if (n >= 0) return 1;
        else return -1;
    }
}

              Created: February 16, 2014
Completed in full by: Michael Yaworski