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?
internal class Program { private static void Main(string[] args) { /* * 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 number that is evenly divisible by all of the numbers from 1 to 20? */ int[] numbers = Enumerable.Range(1, 20).ToArray(); int prime = 2; int nextPrime = 2; int nextPrimePow2 = 2*2; for (int i = 1; nextPrimePow2 < 20; i++) { int n = numbers[i]; if (n == 0) continue; for (int j = i + 1; j < numbers.Length; j++) { int k = numbers[j]; if (k%prime == 0) { numbers[j] = 0; continue; } if (prime == nextPrime) nextPrime = k; } prime = nextPrime; nextPrimePow2 = nextPrime*nextPrime; } var primes = numbers.Where(p => p != 0 && p != 1).ToArray(); var primeNums = new int[primes.Length]; numbers = Enumerable.Range(1, 20).ToArray(); for (int i = 0; i < numbers.Length; i++) { int n = numbers[i]; for (int j = 0; j < primes.Length; j++) { int item = primes[j]; int k = 0; for (; ; k++, n /= item) { if (n % item != 0) break; } if (primeNums[j] < k) primeNums[j] = k; } } long result = 1; for (int i = 0; i < primes.Length; i++) { Console.WriteLine("{0}*{1}", primes[i], primeNums[i]); result *= (long)Math.Pow(primes[i],primeNums[i]); } Console.WriteLine(result); } }