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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.io.*;
import java.util.*;
//import java.util.Map.Entry;
//import java.util.stream.*;
//import java.math.*;

public class Main {

    public static void main(String[] args) throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        Scanner sc = new Scanner(System.in);
        long MOD = (long) (Math.pow(10, 9) + 7);
        int n = sc.nextInt();
        long ans = 1;
        while (n-- > 0) {
            long a = sc.nextLong();
            ans = lcm(ans, a);
        }
        System.out.println(ans);
        bw.flush();
    }
//==============================================//
//==============================================//
//==============================================//
//==============================================//
//==============================================//
//==============================================//
//==============================================//
//==============================================//

    static class Pair implements Comparable<Pair> {

        int a, b;

        public Pair(int x, int y) {
            a = x;
            b = y;
        }

        @Override
        public int compareTo(Pair p) {
            return a - p.a;
        }
    }

    static void forl_0(int n, int[] array, Scanner sc) {
        for (int i = 0; i < n; i++) {
            array[i] = sc.nextInt();
        }
    }

    static void forl_1(int n, int[] array, Scanner sc) {
        for (int i = 1; i <= n; i++) {
            array[i] = sc.nextInt();
        }
    }

    static void two_d(int n, int m, int[][] array, Scanner sc) {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                array[i][j] = sc.nextInt();
            }
        }
    }

    static boolean isPrime(long n) {
        if (n < 2) {
            return false;
        } else if (n == 2 || n == 3) {
            return true;
        } else if (n % 2 == 0 || n % 3 == 0) {
            return false;
        }
        long sqrtN = (long) Math.sqrt(n) + 1;
        for (long i = 6L; i <= sqrtN; i += 6) {
            if (n % (i - 1) == 0 || n % (i + 1) == 0) {
                return false;
            }
        }
        return true;
    }

    public static long gcd(long a, long b) {
        return (b == 0) ? a : gcd(b, a % b);
    }

    public static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }
}