# 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;
}
}
```