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.Linq;

public static partial class Program
{
    //テンプレここから
    public static int ToInt(this string str) => int.Parse(str);
    public static long ToLong(this string str) => long.Parse(str);
    public static int[] ToInt(this string[] strs) => strs.Select(x => x.ToInt()).ToArray();
    public static long[] ToLong(this string[] strs) => strs.Select(x => x.ToLong()).ToArray();
    public static int[] SplToInt(this string str, char opr = ' ') => str.Split(opr).ToInt();
    public static long[] SplToLong(this string str, char opr = ' ') => str.Split(opr).ToLong();
    public static string CRL() => Console.ReadLine();
    public static void CWL(object obj) => Console.WriteLine(obj);
    public static int Diff(int a, int b) => (int)Diff(a, (long)b);
    public static long Diff(long a, long b) => Math.Abs(Math.Max(a, b) - Math.Min(a, b));
    public static int Sign(this int i) => Math.Sign(i);
    public static bool IsEven(this int i) => i % 2 == 0;
    public static int[] dx = new int[] { 0, -1, 0, 1 };
    public static int[] dy = new int[] { -1, 0, 1, 0 };
    public static int[] ToFlat(this int[] array) => array.Cast<long>().ToArray().ToFlat().Cast<int>().ToArray();
    public static long[] ToFlat(this long[] array)
    {
        var min = array.Min();
        return array.Select(x => x - min).ToArray();
    }
    public static int Gcd(int a, int b) => (int)Gcd(a, (long)b);
    public static long Gcd(long a, long b)
    {
        if (b == 0)
        {
            return a;
        }

        return Gcd(b, a % b);
    }
    public static int Lcm(int a, int b) => (int)Lcm(a, (long)b);
    public static long Lcm(long a, long b) => a / Gcd(a, b) * b;
    //テンプレここまで
}

public static partial class Program
{
    static void Main()
    {
        var n = CRL().ToInt();
        long ans = 0;
        for (int i = 0; i < n; i++)
        {
            var input = CRL().ToLong();
            if (ans == 0)
            {
                ans = input;
                continue;
            }

            ans = Lcm(ans, input);
        }

        CWL(ans);
    }
}