#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int t;
  cin >> t;
  while (t--) {
    ll a, b, k;
    cin >> a >> b >> k;
    const ll l = lcm(a, b);
    ll lo = 0, hi = 4e18;
    while (hi - lo > 1) {
      const ll x = (hi + lo) / 2;
      ll cnt = x - (x / a) - (x / b) + (x / l);
      (cnt >= k ? hi : lo) = x;
    }
    cout << hi << '\n';
  }
  return 0;
}