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-csc 3.5.0) (judge verdict: Accepted)

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

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC070.C();
    }
    class ABC070
    {
      public static void A()
      {
        var N = Read.Str();
        Console.WriteLine(N[0] == N[2] ? "Yes" : "No");
      }
      public static void B()
      {
        var A = Read.Int();
        var B = Read.Int();
        var C = Read.Int();
        var D = Read.Int();
        var S = Math.Max(A, C);
        var T = Math.Min(B, D);
        Console.WriteLine(Math.Max(0, T - S));
      }
      public static void C()
      {
        var N = Read.Int();
        var T = Enumerable.Range(0, N).Select(i => Read.Long()).ToArray();
        var lcm = T[0];
        for(int i = 1; i < N; ++i)
        {
          var gcd = Util.GCD(lcm, T[i]);
          lcm = lcm / gcd * T[i];
        }
        Console.WriteLine(lcm);
      }
      public static void D()
      {
        var N = Read.Int();
        var Adj = Read.AdjacencyListWithWeight(N, N - 1);
        var Q = Read.Int();
        var K = Read.Int();
        var XY = Read.TupleInt(Q);
        var dist = Graph.CalcDistance_OnTree(Adj, N, K);
        var ans = new List<long>();
        foreach(var xy in XY)
        {
          ans.Add(dist[xy.Item1] + dist[xy.Item2]);
        }
        Console.WriteLine(String.Join(Environment.NewLine, ans));
      }
    }
    class Util
    {
      public static T[,] Gen<T>(int r, int c, T v)
      {
        var matrix = new T[r, c];
        for (int i = 0; i < r; ++i)
        {
          for (int j = 0; j < c; ++j)
          {
            matrix[i, j] = v;
          }
        }
        return matrix;
      }
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static long[,] ASum(long[,] matrix)
      {
        var N = matrix.GetLength(0);
        var M = matrix.GetLength(1);
        var res = new long[N + 1, M + 1];
        for(int i = 0; i < N; ++i)
        {
          for(int j = 0; j < M; ++j)
          {
            res[i + 1, j + 1] = res[i, j + 1] + res[i + 1, j] - res[i, j] + matrix[i, j];
          }
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }
      public static long GCD(long a, long b)
      {
        while (b > 0)
        {
          var c = a % b;
          a = b;
          b = c;
        }
        return a;
      }
    }
    class Graph
    {
      public static HashSet<int> ConnectedComponent(Dictionary<int, HashSet<int>> adj, int idx)
      {
        HashSet<int> comp = new HashSet<int>();
        comp.Add(idx);
        List<int> target = new List<int>();
        target.Add(idx);
        while (target.Count > 0)
        {
          List<int> next = new List<int>();
          foreach (var p in target)
          {
            foreach (var f in adj[p])
            {
              if (!comp.Contains(f))
              {
                next.Add(f);
                comp.Add(f);
              }
            }
          }
          target = next;
        }
        return comp;
      }
      public static int[] CalcDistance_OnTree(Dictionary<int, HashSet<int>> adj, int N, int start)
      {
        var dist = Enumerable.Range(0, N + 1).Select(i => -1).ToArray();
        dist[start] = 0;
        Queue<int> queue = new Queue<int>();
        queue.Enqueue(start);
        while (queue.Count > 0)
        {
          var v = queue.Dequeue();
          foreach (var w in adj[v])
          {
            if (dist[w] < 0)
            {
              dist[w] = dist[v] + 1;
              queue.Enqueue(w);
            }
          }
        }
        return dist;
      }
      public static long[] CalcDistance_OnTree(Dictionary<int, Dictionary<int, long>> adj, int N, int start)
      {
        var dist = Enumerable.Range(0, N + 1).Select(i => -1L).ToArray();
        dist[start] = 0;
        Queue<int> queue = new Queue<int>();
        queue.Enqueue(start);
        while (queue.Count > 0)
        {
          var v = queue.Dequeue();
          foreach (var t in adj[v])
          {
            var w = t.Key;
            var c = t.Value;
            if (dist[w] < 0)
            {
              dist[w] = dist[v] + c;
              queue.Enqueue(w);
            }
          }
        }
        return dist;
      }
    }

    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}