using System;
using System.Linq;
using System.Collections;
using System.IO;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.Runtime.Intrinsics.X86;
using System.Buffers;
using System.Diagnostics;
using System.Runtime.CompilerServices;
using static InputUtility;

class Program
{
    static void Main()
    {
        using Output output = new(false);

        InputNewLine();
        var t = NextInt32;

        for (int i = 0; i < t; i++)
        {
            Solve();
        }
    }

    private static void Solve()
    {
        InputNewLine();
        var (a, b, k) = ((ulong)NextInt64, (ulong)NextInt64, (ulong)NextInt64);

        var lcm = Lcm(a, b);

        ulong ok = ulong.MaxValue >> 2;
        var ng = 0UL;
        while (ok - ng > 1)
        {
            var mid = (ok + ng) / 2;
            if (mid - DivisibleCount(mid) >= k)
            {
                ok = mid;
            }
            else
            {
                ng = mid;
            }
        }

        ulong DivisibleCount(ulong k) => k / a + k / b - k / lcm;

        Console.WriteLine(ok);
    }

    public static ulong Gcd(ulong a, ulong b) => b == 0 ? a : Gcd(b, a % b);

    public static ulong Lcm(ulong a, ulong b) => a / Gcd(a, b) * b;

}

public static class InputUtility
{
    private static string[]? s_inputs;
    private static string? s_raw;
    private static int s_index = 0;

    private static void Init() => s_index = 0;
    public static int NextInt32 => int.Parse(s_inputs![s_index++]!);
    public static uint NextUInt32 => uint.Parse(s_inputs![s_index++]!);
    public static long NextInt64 => long.Parse(s_inputs![s_index++]!);
    public static BigInteger NextBigInteger => long.Parse(s_inputs![s_index++]!);
    public static string NextString => s_inputs![s_index++];
    public static char NextChar => s_inputs![s_index++][0];
    public static int[] GetInt32Array() => s_inputs!.Select(int.Parse).ToArray();
    public static long[] GetInt64Array() => s_inputs!.Select(long.Parse).ToArray();
    public static string GetRawString() => s_raw!;
#if DEBUG
    private static TextReader? s_textReader;
    public static void SetSource(string path) => s_textReader = new StringReader(File.ReadAllText(path));
#endif
    public static bool InputNewLine()
    {
#if DEBUG
        if (s_textReader is TextReader sr)
        {
            Init();
            s_raw = sr.ReadLine()!;
            s_inputs = s_raw.Split(' ', StringSplitOptions.RemoveEmptyEntries);
            return true;
        }
#endif
        Init();
        s_raw = Console.ReadLine()!;
        s_inputs = s_raw.Split(' ', StringSplitOptions.RemoveEmptyEntries);
        return true;
    }
}

public readonly struct Output : IDisposable
{
    private readonly StreamWriter _sw;
#if DEBUG
    public Output(string path)
    {
        var fs = new FileStream(path, FileMode.Create, FileAccess.Write);
        _sw = new StreamWriter(fs);
        Console.SetOut(_sw);
    }
#endif
    public Output(bool autoFlush)
    {
        _sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = autoFlush };
        Console.SetOut(_sw);
    }

    public void Dispose()
    {
        _sw.Dispose();
    }

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    internal void Flush()
    {
        _sw.Flush();
    }
}

public static class ArrayExtensions
{
    public static void Swap<T>(this T[] array, int i, int j) => (array[i], array[j]) = (array[j], array[i]);

    public static int LowerBound<T>(this T[] a, T target) where T : IComparable<T>
    {
        int ok = a.Length;
        int ng = -1;

        while (Math.Abs(ok - ng) > 1 && (ok + ng) / 2 is int mid)
            (ok, ng) = a[mid].CompareTo(target) >= 0 ? (mid, ng) : (ok, mid);

        return ok;
    }

    public static int UpperBound<T>(this T[] a, T target) where T : IComparable<T>
    {
        int ok = a.Length;
        int ng = -1;

        while (Math.Abs(ok - ng) > 1 && (ok + ng) / 2 is int mid)
            (ok, ng) = a[mid].CompareTo(target) > 0 ? (mid, ng) : (ok, mid);

        return ok;
    }

    public struct IndexedEnumerable<T> : IEnumerable<(T item, int index)>
    {
        private readonly T[] _a;
        private readonly int _startIndex;

        public IndexedEnumerable(T[] a, int startIndex = 0)
        {
            _a = a;
            _startIndex = startIndex;
        }

        public readonly IndexedEnumerator<T> GetEnumerator() => new IndexedEnumerator<T>(_a, _startIndex);
        IEnumerator IEnumerable.GetEnumerator() => GetEnumerator();
        IEnumerator<(T item, int index)> IEnumerable<(T item, int index)>.GetEnumerator() => GetEnumerator();
    }

    public struct IndexedEnumerator<T> : IEnumerator<(T item, int index)>
    {
        public readonly (T item, int index) Current => (_a[_index], _index + _startIndex);

        private int _index;
        private int _startIndex;
        private T[] _a;

        public IndexedEnumerator(T[] a, int startIndex)
        {
            _index = -1;
            _a = a;
            _startIndex = startIndex;
        }

        public bool MoveNext() => ++_index < _a.Length;
        readonly object IEnumerator.Current => Current;
        public readonly void Dispose() { }
        public void Reset() => _index = -1;
    }

    /// <returns>(T value, int index)</returns>
    public static IndexedEnumerable<T> Enumerate<T>(this T[] arr, int startIndex = 0) => new IndexedEnumerable<T>(arr, startIndex);
}

public static class IEnumerableExtensions
{
    public static IEnumerable<TSource> Log<TSource>(this IEnumerable<TSource> source)
    {
        Console.WriteLine(string.Join(' ', source));
        return source;
    }

    public static ScanEnumerable<TSource, TAccumulate> Scan<TSource, TAccumulate>(
        this IEnumerable<TSource> source,
        TAccumulate seed,
    Func<TAccumulate, TSource, TAccumulate> accumulator) where TSource : struct where TAccumulate : struct
    {
        return new ScanEnumerable<TSource, TAccumulate>(source, accumulator, seed);
    }

    public static IEnumerable<TAccumulate> ScanExSeed<TSource, TAccumulate>(
        this IEnumerable<TSource> source,
        TAccumulate seed,
        Func<TAccumulate, TSource, TAccumulate> accumulator)
    {
        var accumulation = new List<TAccumulate>();

        var current = seed;
        foreach (var item in source)
        {
            current = accumulator(current, item);
            accumulation.Add(current);
        }

        return accumulation;
    }

    public readonly struct ScanEnumerable<TSource, TAccumulate> : IEnumerable<TAccumulate> where TSource : struct where TAccumulate : struct
    {
        private readonly IEnumerable<TSource> _source;
        private readonly Func<TAccumulate, TSource, TAccumulate> _accumulator;
        private readonly TAccumulate _seed;

        public ScanEnumerable(IEnumerable<TSource> source, Func<TAccumulate, TSource, TAccumulate> accumulator, TAccumulate seed)
        {
            _source = source;
            _accumulator = accumulator;
            _seed = seed;
        }

        public readonly ScanEnumerator<TSource, TAccumulate> GetEnumerator() => new(_source, _accumulator, _seed);
        readonly IEnumerator IEnumerable.GetEnumerator() => GetEnumerator();
        readonly IEnumerator<TAccumulate> IEnumerable<TAccumulate>.GetEnumerator() => GetEnumerator();
    }

    public struct ScanEnumerator<TSource, TAccumulate> : IEnumerator<TAccumulate> where TSource : struct where TAccumulate : struct
    {
        private readonly Func<TAccumulate, TSource, TAccumulate> _accumulator;

        private readonly IEnumerator<TSource> _enumerator;
        private TAccumulate _current;

        private bool _secondOrLaterElement = false;

        public ScanEnumerator(IEnumerable<TSource> source, Func<TAccumulate, TSource, TAccumulate> accumulator, TAccumulate seed)
        {
            _enumerator = source.GetEnumerator();
            _accumulator = accumulator;

            _current = seed;
        }

        public readonly TAccumulate Current => _current;
        readonly object IEnumerator.Current => Current;

        public readonly void Dispose() { }

        public bool MoveNext()
        {
            if (_secondOrLaterElement)
            {
                if (_enumerator.MoveNext())
                {
                    _current = _accumulator(_current, _enumerator.Current);
                    return true;
                }
                return false;
            }
            else
            {
                _secondOrLaterElement = true;
                return true;
            }
        }

        public void Reset()
        {
            throw new NotSupportedException();
        }
    }

    public static IEnumerable<TSource> Scan<TSource>(
        this IEnumerable<TSource> source,
        Func<TSource, TSource, TSource> accumulator)
    {
        if (source is null)
            throw new ArgumentNullException(paramName: nameof(source));

        if (accumulator is null)
            throw new ArgumentNullException(paramName: nameof(accumulator));

        var accumulation = new List<TSource>();

        if (source.Any() is false)
        {
            return accumulation;
        }

        var current = source.First();
        accumulation.Add(current);

        foreach (var item in source.Skip(1))
        {
            current = accumulator(current, item);
            accumulation.Add(current);
        }

        return accumulation;
    }
}

public class MyMath
{
    public static long Pow(long x, int y) => Enumerable.Repeat(x, y).Aggregate(1L, (acc, x) => acc * x);
    public static long Pow10(int y) => Pow(10, y);
    public static long Pow2(int y) => Pow(2, y);
}

public class MyMathBigInteger
{
    public static BigInteger Pow(long x, int y) => Enumerable.Repeat(x, y).Aggregate(new BigInteger(1), (acc, x) => acc * x);
    public static BigInteger Pow10(int y) => Pow(10, y);
    public static BigInteger Pow2(int y) => Pow(2, y);
}