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.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Threading.Tasks;

class Program
{

	//最大公約数を求める関数（Gratest Common Divisor）
	//タイプはulongとする
	static ulong GCD(ulong a, ulong b)
	{
		//より大きい方をnとする
		ulong n = Math.Max(a, b);
		ulong m = Math.Min(a, b);

		//ループ処理（ユークリッドの互除法を利用）
		while(m != 0){
			ulong rem = n % m;
			n = m;
			m = rem;
		}

		return n;
	}

	//最小公倍数を求める関数（Least Common Multiple）
	/*
	GCD(a,b) * LCM(a,b) = ab、という性質を利用
	即ち、LCM(a,b) = ab / GCD(a,b)である。
	*/
	static ulong LCM(ulong a, ulong b){
		ulong lcm = 0;

		//より大きい方をnとする
		ulong n = Math.Max(a, b);
		ulong m = Math.Min(a, b);

		//最大公約数
		/*
		当然だが、gcdはnの約数なので、n/gcdは適当
		*/
		ulong gcd = GCD(n,m);
		lcm = n / gcd * m;

		return lcm;
	}

	//Main
	static void Main(string[] args)
	{
		//読み込む
		int N = int.Parse(Console.ReadLine());
		ulong ans = 1;

		//毎回、最小公倍数を求める
		for(int i=0; i<N; i++){
			ulong T = ulong.Parse(Console.ReadLine());
			ans = LCM(ans,T);
		}

		Console.WriteLine(ans);

	}
}