Problem:
Score : 300 points

Problem Statement

We have N clocks. The hand of the i-th clock (1≤i≤N) rotates through 360° in exactly T_i seconds.

Initially, the hand of every clock stands still, pointing directly upward.

Now, Dolphin starts all the clocks simultaneously.

In how many seconds will the hand of every clock point directly upward again?

Constraints

1≤N≤100

1≤T_i≤10^{18}

All input values are integers.

The correct answer is at most 10^{18} seconds.

Input

Input is given from Standard Input in the following format:

N
T_1
:
T_N

Output

Print the number of seconds after which the hand of every clock point directly upward again.

Sample Input 1

2
2
3

Sample Output 1

6

We have two clocks. The time when the hand of each clock points upward is as follows:

Clock 1: 2, 4, 6, ... seconds after the beginning

Clock 2: 3, 6, 9, ... seconds after the beginning

Therefore, it takes 6 seconds until the hands of both clocks point directly upward.

Sample Input 2

5
2
5
10
1000000000000000000
1000000000000000000

Sample Output 2

1000000000000000000

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            //[summary]C - Multiple Clocks
            int n = int.Parse(Console.ReadLine());
            var t = ReadLines(n);

            long lcm = t[0];

            for (int i = 1; i < n; i++)
            {
                long newLcm = GetLcm(lcm, t[i]);

                if (newLcm == 0)
                {
                    lcm = GetLcmByFactoring(lcm, t[i]);
                }
                else
                {
                    lcm = newLcm;
                }
            }

            Console.WriteLine(lcm);
        }

        static long GetLcm(long a, long b)
        {
            if (a >= b)
            {
                if (a % b == 0)
                {
                    return a;
                }
            }
            else
            {
                if (b % a == 0)
                {
                    return b;
                }
            }

            return 0;
        }

        static long GetLcmByFactoring(long a, long b)
        {
            long upper = (long)Math.Pow(10, 9);
            long gcd = GetGcd(a, b);

            if (a <= upper && b <= upper)
            {
                return a * b / gcd;
            }
            else
            {
                var lib = new Library.Factorization();

                var factorsA = lib.GetFactors(a);
                var factorsB = lib.GetFactors(b);
                factorsA.AddRange(factorsB);

                var factorsGcd = lib.GetFactors(gcd);

                for(int i = 0; i < factorsGcd.Count; i++)
                {
                    factorsA.Remove(factorsGcd[i]);
                }

                //foreach (var factor in factorsGcd)
                //{
                //    factorsA.Remove(factor);
                //}

                long lcm = 1;

                foreach (var factor in factorsA)
                {
                    lcm *= factor;
                }

                return lcm;
            }
        }

        static long GetGcd(long a, long b)
        {
            var lib = new Library.Gcd();
            return lib.GetGcd(a, b);
        }

        static List<long> ReadLines(long count = 0)
        {
            //[summary]コンソールの値を読み込む
            var lines = new List<long>();
            string s;

            //読み込む行数が未指定のときは、1行目の値を"count"とみなす
            if (count == 0)
            {
                s = Console.ReadLine().TrimEnd();
                count = long.Parse(s);
            }

            for (long i = 0; i < count; i++)
            {
                s = Console.ReadLine().TrimEnd();
                lines.Add(long.Parse(s));
            }

            return lines;
        }
    }
}

namespace Library
{
    public class Gcd
    {
        public long GetGcd(long a, long b)
        {
            //[summary]a,b2つの数の最大公約数を求める
            //以下リンクを参考に実装
            //https://qiita.com/gushwell/items/e9614b4ac2bea3fc6486

            if (a < b)
            {
                //引数を入れ替えて自分を呼び出す
                return GetGcd(b, a);
            }
            else
            {
                while (b > 0)
                {
                    long remainder = a % b;

                    a = b;
                    b = remainder;
                }

                return a;
            }
        }

        public long GetLcm(long a, long b)
        {
            //[summary]a,b2つの数の最小公倍数を求める
            //Lcm: least Common Multiple
            //以下リンクを参考に実装
            //https://qiita.com/gushwell/items/f08d0e71fa0480dbb396

            long gcd = GetGcd(a, b);
            return a * b / gcd;
        }
    }

    class Factorization
    {
        private List<long> factors = new List<long>();

        public List<long> GetFactors(long n)
        {
            //[summary]ある数を素因数分解する

            if (n < 2)
            {
                //2より小さい数を受け取った場合
                factors.Add(n);
            }
            else
            {
                Factoring(n);
            }

            return factors;
        }

        private void Factoring(long n)
        {
            //[summary]平方根以下の素数で総当りで割って行く
            //以下リンクを参考に実装
            //https://qiita.com/gushwell/items/561afde2e00bf3380c98

            //平方根を求める
            long sqrt = (long)Math.Sqrt(n);

            //2,3,5で割る(割れなくなるまで割り続ける)
            n = DevideWith(n, 2);
            n = DevideWith(n, 3);
            n = DevideWith(n, 5);

            var primes = new List<int> { 7, 11, 13, 17, 19, 23, 29, 31 };
            long i = 0;

            //平方根以下の素数(候補)で総当りで割る
            while (n > 1)
            {
                foreach (var p in primes)
                {
                    if (p + i > sqrt)
                    {
                        factors.Add(n);
                        return;
                    }
                    else
                    {
                        n = DevideWith(n, p + i);
                    }
                }

                i += 30;
            }
        }

        private long DevideWith(long n, long d)
        {
            while (n % d == 0)
            {
                factors.Add(d);
                n /= d;
            }

            return n;
        }
    }
}