#include <iostream>
#include <string>
#include <vector>

using namespace std;

void getNumbers(string line, vector<int>& numbers);
long long simpleLCM(long long& lcm, int f, int n);
long long primeLCM(vector<int> numbers, long long lcm);
int getPrime(int n);

int main()
{
    int a = 0, f, n, o;
    long long lcm = 1;
    string line;
    vector<int> numbers;
    cout << "Choose with what numbers you want to find LCM" << endl;
    cout << "1. From 1 to specific number" << endl;
    cout << "2. From specific number to specific number" << endl;
    cout << "3. Several seperate numbers" << endl;
    while (true)
    {
        cin >> o;
        switch (o)
        {
        case 1:
            cout << "Enter specific number" << endl;
            cin >> n;
            f = 1;
            lcm = simpleLCM(lcm, f, n);
            goto loc2;
        case 2:
            cout << "Enter 1st specific number" << endl;
            cin >> f;
            cout << "Enter 2nd specific number" << endl;
            cin >> n;
            for (int i = f; i <= n; i++)
                numbers.push_back(i);
            goto loc1;
        case 3:
            cout << "Enter several numbers seperated by a space" << endl;
            cin.ignore();
            getNumbers(line, numbers);
            goto loc1;
        default:
            cout << "Your option is invalid" << endl;
            break;
        }
    }
    loc1:
    lcm = primeLCM(numbers, lcm);
    loc2:
    cout << lcm << endl;
    return 0;
}
void getNumbers(string line, vector<int>& numbers)
{
    string s = "";
    getline(cin, line);
    for (auto x : line) {
        if (x == ' ')
        {
            numbers.push_back(stoi(s));
            s = "";
        }
        else
            s = s + x;
    }
    numbers.push_back(stoi(s));
}
long long simpleLCM(long long& lcm, int f, int n)
{
    vector<long long> list;
    for (int i = f; i <= n; i++)
    {
        list.push_back(i);
        if (lcm % i == 0)
            continue;
        lcm *= i;
        for (size_t ii = 0; ii < list.size() - 1; ii++)
        {
            if (i % list[ii] == 0)
            {
                lcm /= list[ii];
                list.erase(list.begin() + ii);
            }
        }
    }
    return lcm;
}
long long primeLCM(vector<int> numbers, long long lcm)
{
    bool divided = false;
    int prime = 2;
    int n = 2;
    while (true)
    {
        for (size_t i = 0; i < numbers.size(); i++)
        {
            if (numbers[i] != 1)
                goto loc2;
        }
        return lcm;
        loc2:
        for (size_t i = 0; i < numbers.size(); i++)
        {
            if (numbers[i] % prime == 0)
            {
                numbers[i] /= prime;
                divided = true;
            }
        }
        if (divided == true)
        {
            lcm *= prime;
            divided = false;
        }
        else
        {
            prime = getPrime(n);
            n++;
        }
    }
}
int getPrime(int n)
{
    int p = 1;
    for (int i = 3; ; i += 2)
    {
        for (int j = 3; j < i; j += 2)
        {
            if (i % j == 0)
                goto loc3;
        }
        p++;
        loc3:
        if (p == n)
            return i;
    }
}