using System;
using System.Collections.Generic;

namespace ProjectEulerMyAnswers.Solves
{
    class Problem_5_alt
    {
        int number = 0;

        public Problem_5_alt(int num)
        {
            Console.WriteLine(GetAnswer(Factoring(num)));
        }

        bool IsPrime(int num)
        {
            for (int i = 2; i <= num / 2; i++) {
                if (num % i == 0) {
                    return false;
                }
            }
            return true;
        }

        List<int> Factoring(int n)
        {
            List<int> FactorsOfNum = new List<int>();
            int pow = 0;
            for (int i = 2; i <= n; i++)
            {
                if (IsPrime(i))
                {
                    int num = i;
                    while(num <= n)
                    {
                        num *= i;
                        pow++;
                    }
                    number = num;
                    FactorsOfNum.Add(pow);
                }
            }
            return FactorsOfNum;
        }

        ulong GetAnswer(List<int> Factors)
        {
            ulong Answer = 1;
            for(int i = 0; i < Factors.Count; i++)
            {
                Answer *= Convert.ToUInt64(Math.Pow(number, Factors[i]));
            }
            return Answer;
        }
    }
}