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);

        }

    }