using System;
using static System.Console;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static int NN => int.Parse(ReadLine());
    static long[] NList => ReadLine().Split().Select(long.Parse).ToArray();
    public static void Main()
    {
        Solve();
    }
    static void Solve()
    {
        var t = NN;
        var ans = new long[t];
        for (var u = 0; u < t; ++u)
        {
            var c = NList;
            var (a, b, k) = (c[0], c[1], c[2]);
            ans[u] = Divisible(a, b, k);
        }
        WriteLine(string.Join("\n", ans));
    }
    static long Divisible(long a, long b, long k)
    {
        var gcd = GCD(a, b);
        var lcm = a / gcd * b;
        var ok = 8_000_000_000_000_000_000;
        var ng = 0L;
        while (ok - ng > 1)
        {
            var mid = (ok + ng) / 2;
            var cnt = mid - mid / a - mid / b + mid / lcm;
            if (cnt >= k) ok = mid;
            else ng = mid;
        }
        return ok;
    }
    static long GCD(long a, long b)
    {
        if (a < b) return GCD(b, a);
        if (a % b == 0) return b;
        return GCD(b, a % b);
    }
}