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.Generic;
using System.IO;
using System.Linq;
using static System.Math;
using System.Text;
using System.Threading;
using System.Globalization;
using System.Runtime.CompilerServices;
using Library;

namespace Program
{
    public static class ProblemB
    {
        static bool SAIKI = false;
        static public int numberOfRandomCases = 0;
        static public void MakeTestCase(List<string> _input, List<string> _output, ref Func<string[], bool> _outputChecker)
        {
        }
        static public void Solve()
        {
            var N = NN;
            var TList = NNList(N);
            var lcm = 1L;
            foreach (var item in TList) {
                lcm = LIB_Math.LCM(item, lcm);
            }
            Console.WriteLine(lcm);
        }
        class Printer : StreamWriter
        {
            public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
            public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { base.AutoFlush = false; }
            public Printer(Stream stream, Encoding encoding) : base(stream, encoding) { base.AutoFlush = false; }
        }
        static LIB_FastIO fastio = new LIB_FastIODebug();
        static public void Main(string[] args) { if (args.Length == 0) { fastio = new LIB_FastIO(); Console.SetOut(new Printer(Console.OpenStandardOutput())); } if (SAIKI) { var t = new Thread(Solve, 134217728); t.Start(); t.Join(); } else Solve(); Console.Out.Flush(); }
        static long NN => fastio.Long();
        static double ND => fastio.Double();
        static string NS => fastio.Scan();
        static long[] NNList(long N) => Repeat(0, N).Select(_ => NN).ToArray();
        static double[] NDList(long N) => Repeat(0, N).Select(_ => ND).ToArray();
        static string[] NSList(long N) => Repeat(0, N).Select(_ => NS).ToArray();
        static long Count<T>(this IEnumerable<T> x, Func<T, bool> pred) => Enumerable.Count(x, pred);
        static IEnumerable<T> Repeat<T>(T v, long n) => Enumerable.Repeat<T>(v, (int)n);
        static IEnumerable<int> Range(long s, long c) => Enumerable.Range((int)s, (int)c);
        static IOrderedEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x, _ => xorshift);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x) => Enumerable.OrderBy(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderBy<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderBy(x.OrderByRand(), selector);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x) => Enumerable.OrderByDescending(x.OrderByRand(), e => e);
        static IOrderedEnumerable<T1> OrderByDescending<T1, T2>(this IEnumerable<T1> x, Func<T1, T2> selector) => Enumerable.OrderByDescending(x.OrderByRand(), selector);
        static IOrderedEnumerable<string> OrderBy(this IEnumerable<string> x) => x.OrderByRand().OrderBy(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderBy<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderBy(selector, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<string> OrderByDescending(this IEnumerable<string> x) => x.OrderByRand().OrderByDescending(e => e, StringComparer.OrdinalIgnoreCase);
        static IOrderedEnumerable<T> OrderByDescending<T>(this IEnumerable<T> x, Func<T, string> selector) => x.OrderByRand().OrderByDescending(selector, StringComparer.OrdinalIgnoreCase);
        static uint xorshift { get { _xsi.MoveNext(); return _xsi.Current; } }
        static IEnumerator<uint> _xsi = _xsc();
        static IEnumerator<uint> _xsc() { uint x = 123456789, y = 362436069, z = 521288629, w = (uint)(DateTime.Now.Ticks & 0xffffffff); while (true) { var t = x ^ (x << 11); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); yield return w; } }
    }
}
namespace Library {
    class LIB_Math
    {
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public IEnumerable<long> Primes(long x)
        {
            if (x < 2) yield break;
            yield return 2;
            var halfx = x / 2;
            var table = new bool[halfx + 1];
            var max = (long)(Math.Sqrt(x) / 2);
            for (long i = 1; i <= max; ++i)
            {
                if (table[i]) continue;
                var add = 2 * i + 1;
                yield return add;
                for (long j = 2 * i * (i + 1); j <= halfx; j += add)
                    table[j] = true;
            }
            for (long i = max + 1; i <= halfx; ++i)
                if (!table[i] && 2 * i + 1 <= x)
                    yield return 2 * i + 1;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public IEnumerable<long> Factors(long x)
        {
            if (x < 2) yield break;
            while (x % 2 == 0)
            {
                x /= 2; yield return 2;
            }
            var max = (long)Math.Sqrt(x);
            for (long i = 3; i <= max; i += 2)
            {
                while (x % i == 0)
                {
                    x /= i; yield return i;
                }
            }
            if (x != 1) yield return x;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public IEnumerable<long> Divisor(long x)
        {
            if (x < 1) yield break;
            var max = (long)Math.Sqrt(x);
            for (long i = 1; i <= max; ++i)
            {
                if (x % i != 0) continue;
                yield return i;
                if (i != x / i) yield return x / i;
            }
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public long GCD(long a, long b)
        {
            while (b > 0)
            {
                var tmp = b;
                b = a % b;
                a = tmp;
            }
            return a;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public long LCM(long a, long b) => a / GCD(a, b) * b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public long Pow(long x, long y)
        {
            long a = 1;
            while (y != 0)
            {
                if ((y & 1) == 1) a *= x;
                if (x < long.MaxValue / x) x *= x;
                y >>= 1;
            }
            return a;
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public decimal Sqrt(decimal x)
        {
            decimal prev, cur = (decimal)Math.Sqrt((double)x);
            do
            {
                prev = cur;
                if (prev == 0) return 0;
                cur = (prev + x / prev) / 2;
            } while (cur != prev);
            return cur;
        }
        static List<long> _fact = new List<long>() { 1 };
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static void Build(long n)
        {
            if (n >= _fact.Count)
                for (int i = _fact.Count; i <= n; ++i) _fact.Add(_fact[i - 1] * i);
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public long Comb(long n, long k)
        {
            Build(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[(int)n] / _fact[(int)(n - k)] / _fact[(int)k];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public long Perm(long n, long k)
        {
            Build(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[(int)n] / _fact[(int)(n - k)];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static public IEnumerable<List<int>> MakePermutation(long n, bool zeroIndexed = true)
        {
            if (n <= 0) throw new Exception();
            var c = new int[n];
            var a = new int[n];
            if (!zeroIndexed) a[0] = 1;
            for (var i = 1; i < n; i++) a[i] = a[i - 1] + 1;
            yield return new List<int>(a);
            for (var i = 0; i < n;)
            {
                if (c[i] < i)
                {
                    if (i % 2 == 0)
                    {
                        var t = a[0]; a[0] = a[i]; a[i] = t;
                    }
                    else
                    {
                        var t = a[c[i]]; a[c[i]] = a[i]; a[i] = t;
                    }
                    yield return new List<int>(a);
                    ++c[i];
                    i = 0;
                }
                else
                {
                    c[i] = 0;
                    ++i;
                }
            }
        }
    }
    class LIB_FastIO
    {
        public LIB_FastIO() { str = Console.OpenStandardInput(); }
        readonly Stream str;
        readonly byte[] buf = new byte[1024];
        int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        char Char()
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b;
        }
        virtual public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        virtual public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        virtual public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
    class LIB_FastIODebug : LIB_FastIO
    {
        Queue<string> param = new Queue<string>();
        string NextString() { if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item); return param.Dequeue(); }
        public LIB_FastIODebug() { }
        public override string Scan() => NextString();
        public override long Long() => long.Parse(NextString());
        public override double Double() => double.Parse(NextString());
    }
}