#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <exception>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>

using namespace std;

using ld = long double;
using ll = long long;
using ull = unsigned long long;

template<class T> using pq = priority_queue<T>;
template<class T> using pqg = priority_queue<T, vector<T>, greater<T>>;

template<class T, class U> inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return 1; } return 0; }
template<class T, class U> inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return 1; } return 0; }

#define all(v) begin(v), end(v)

void solve() {
  ull a, b, k;
  cin >> a >> b >> k;

  if (a < b) swap(a, b);

  auto check = [&]() {
    vector<int> sum;

    for (int i = 1; sum.size() <= k; ++i) {
      if (i % a == 0 || i % b == 0) continue;
      sum.push_back(i);
    }

    return sum[k-1];
  };

  auto f = [&](ull x) {
    ull sum = 0;

    if (a % b == 0) {
      sum += x / b;
    } else {
      sum += x / a;
      sum += x / b;
      sum -= x / lcm(a, b);
    }

    return (x - sum) >= k;
  };

  ull l = 0, r = 2e18 + 10;
  while (r - l > 1) {
    ull m = (l + r) / 2;
    if (f(m)) r = m;
    else l = m;
  }

  // cout << check() << endl;
  // cout << f(15) << endl;
  cout << r << endl;
}

int main(void) {
  int t;
  cin >> t;

  while (t--) solve();

  return 0;
}