欧拉计划 第5题

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);
        }
    }