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; } }DOWNLOAD

Created: February 16, 2014

Completed in full by: Michael Yaworski