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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

namespace ABC070C
{
    class Program
    {
        static void Solve(Input input)
        {
            var n = input.NextInt();
            var t = input.NextLong(n);

            Console.WriteLine(Number.Lcm(t));
        }

        /// <summary>
        /// 最大公約数
        /// 最大公倍数
        /// 拡張ユークリッド互除法
        /// nPm, nCr
        /// </summary>
        static class Number
        {
            /// <summary>
            /// 最大公約数
            /// ユークリッド互除法
            /// </summary>
            /// <param name="a"></param>
            /// <param name="b"></param>
            /// <returns></returns>
            public static long Gcd(long a, long b)
            {
                long r;

                while ((r = a % b) != 0)
                {
                    a = b;
                    b = r;
                }

                return b;
            }

            /// <summary>
            /// 最大公約数
            /// </summary>
            /// <param name="nums"></param>
            /// <returns></returns>
            public static long Gcd(IEnumerable<long> nums)
                => nums.Aggregate((n, next) => n = Gcd(n, next));

            public static int Gcd(IEnumerable<int> nums)
                => (int)Gcd(nums.Select(x => (long)x));

            /// <summary>
            /// 最大公倍数
            /// </summary>
            /// <param name="a"></param>
            /// <param name="b"></param>
            /// <returns></returns>
            public static long Lcm(long a, long b)
                => a / Gcd(a, b) * b;

            /// <summary>
            /// 最大公倍数
            /// </summary>
            /// <param name="nums"></param>
            /// <returns></returns>
            public static long Lcm(IEnumerable<long> nums)
                => nums.Aggregate((n, next) => n = Lcm(n, next));

            public static long Lcm(IEnumerable<int> nums)
                => Lcm(nums.Select(x => (long)x));

            /// <summary>
            /// 拡張ユークリッドの互除法
            /// ax+by = gcd(a,b)の整数解
            /// </summary>
            /// <param name="a"></param>
            /// <param name="b"></param>
            /// <param name="x"></param>
            /// <param name="y"></param>
            /// <returns></returns>
            public static void ExtendedGcd(long a, long b, out long x, out long y)
            {
                long u = 0, v = 1;
                x = 1; y = 0;

                while (b > 0)
                {
                    long q = a / b;
                    long t;

                    t = u;
                    u = x - q * u;
                    x = t;

                    t = v;
                    v = y - q * v;
                    y = t;

                    t = b;
                    b = a - q * b;
                    a = t;
                }
            }

            /// <summary>
            /// ルジャンドルの公式
            /// n!をpで何回割り切れるか
            /// </summary>
            /// <param name="n">正の整数</param>
            /// <param name="p">素数</param>
            /// <returns></returns>
            public static long Legendres(long n, long p)
            {
                long count = 0;
                for (long m = p; m < n; m *= p)
                {
                    count += n / m;
                }

                return count;
            }

            /// <summary>
            /// n!
            /// 12! < int(2^31 - 1) < 13!
            /// 20! < long(2^63 - 1) < 21!
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            public static long Factorial(long n)
            {
                var m = 1L;

                for (long i = 2; i <= n; i++)
                {
                    m *= i;
                }

                return m;
            }

            /// <summary>
            /// nPr
            /// </summary>
            /// <param name="n"></param>
            /// <param name="r"></param>
            /// <returns></returns>
            public static long Permutation(long n, long r)
            {
                var m = n;

                for (long i = n - 1; i > n - r; i--)
                {
                    m *= i;
                }

                return m;
            }

            /// <summary>
            /// nCr
            /// </summary>
            /// <param name="n"></param>
            /// <param name="r"></param>
            /// <returns></returns>
            public static long Combination(long n, long r)
            {
                return Permutation(n, r) / Factorial(r);
            }
        }

        #region Competitive Template
        static readonly int MOD = (int)1e9 + 7;

        public static void Main(string[] args)
        {
            // 出力が少ないときはこれをセットする方が時間かかるけれど
            // その場合は出力がボトルネックになっていないので、まあ良しとする
            var needsFlushOutput = true;
            if (needsFlushOutput)
            {
                // 細かく出力しないようにする
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }

            // 通常は引数無しで、ファイルから読み出したい場合はpath指定する
            var input = new Input();
            // 仮想的に標準入力をセットする
            //input.SetText("");

            Solve(input);

            Console.Out.Flush();
        }

        class Input
        {
            // 変な改行コードがたまに混じっているので、一応セパレート指定する
            // スペース単独指定の方がもちろん早い
            static readonly char[] separator = { ' ', '\r', '\n' };
            Queue<string> q { get; set; }
            StreamReader sr;

            /// <summary>
            /// 特定のファイルから読み出したい場合はpath指定する
            /// </summary>
            /// <param name="path"></param>
            public Input(string path = "")
            {
                q = new Queue<string>();

                if (string.IsNullOrEmpty(path))
                {
                    sr = new StreamReader(Console.OpenStandardInput());
                }
                else
                {
                    sr = new StreamReader(path);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="items"></param>
            public void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="s"></param>
            /// <returns></returns>
            public bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            /// <returns></returns>
            bool read()
            {
                var s = sr.ReadLine();
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                if (!q.Any()) return read();

                return true;
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            /// <returns></returns>
            public string Next()
            {
                if (!q.Any())
                {
                    if (!read())
                    {
                        return "";
                    }
                }

                return q.Dequeue();
            }

            /// <summary>
            /// 指定個数queueにたまるまでenqueueし続ける
            /// </summary>
            /// <param name="n"></param>
            /// <returns></returns>
            bool accumulate(int n)
            {
                while (q.Count() < n)
                {
                    if (!read()) return false;
                }

                return true;
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            /// <summary>
            /// n個の要素をparseして、それぞれにoffsetをaddした配列を返す
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="n"></param>
            /// <param name="offset"></param>
            /// <param name="parse"></param>
            /// <param name="add"></param>
            /// <returns></returns>
            T[] NextT<T>(int n, T offset, Func<string, T> parse, Func<T, T, T> add)
            {
                if (!accumulate(n)) return null;

                var a = new T[n];

                for (int i = 0; i < n; i++)
                    a[i] = add(parse(q.Dequeue()), offset);

                return a;
            }

            public string[] Next(int n) => NextT(n, "", x => x, (x, y) => x);
            public int[] NextInt(int n, int offset = 0) => NextT(n, offset, int.Parse, (x, y) => x + y);
            public long[] NextLong(int n, long offset = 0) => NextT(n, offset, long.Parse, (x, y) => x + y);
            public double[] NextDouble(int n, double offset = 0.0) => NextT(n, offset, double.Parse, (x, y) => x + y);
        }

        static class Utils
        {
            public static void Print<T>(IEnumerable<T> ie, string sep = " ") => Console.WriteLine(string.Join(sep, ie));
            public static void Print<T>(params T[] objs) => Print(objs);
            public static T Max<T>(params T[] objs) => objs.Max();
            public static T Min<T>(params T[] objs) => objs.Min();

            public static void Swap<T>(ref T x, ref T y) where T : struct { var t = x; x = y; y = t; }
            public static void Swap<T>(IList<T> list, int i, int j) where T : struct { var t = list[i]; list[i] = list[j]; list[j] = t; }

            /// <summary>
            /// vでfillされたT[d1][d2]配列を作成する
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="d1"></param>
            /// <param name="d2"></param>
            /// <param name="v"></param>
            /// <returns></returns>
            public static T[][] Create2DArray<T>(int d1, int d2, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(v, d2).ToArray()).ToArray();
            }

            /// <summary>
            /// vでfillされたT[d1][d2][d3]配列を作成する
            /// </summary>
            /// <typeparam name="T"></typeparam>
            /// <param name="d1"></param>
            /// <param name="d2"></param>
            /// <param name="d3"></param>
            /// <param name="v"></param>
            /// <returns></returns>
            public static T[][][] Create3DArray<T>(int d1, int d2, int d3, T v = default(T))
            {
                return
                    Enumerable.Repeat(0, d1).Select(_ =>
                    Enumerable.Repeat(0, d2).Select(__ =>
                     Enumerable.Repeat(v, d3).ToArray()).ToArray()).ToArray();
            }
        }
        #endregion
    }
}