#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
using namespace std;
int main() {
  cin.tie(0); cout.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);
  int T;
  cin >> T;
  while(T--) {
    long long A, B, K;
    cin >> A >> B >> K;
    long long D = lcm(A, B);
    long long C = D - D / A - D / B + 1;
    long long ans = K / C * D;
    K %= C;
    long long ok = 0, ng = D + 1;
    while(abs(ok - ng) > 1) {
      long long mid = (ok + ng) >> 1;
      long long cnt = mid - mid / A - mid / B;
      if(cnt > K) {
        ng = mid;
      } else {
        ok = mid;
      }
    }
    if(K == 0) {
      while(ans % A == 0 || ans % B == 0) {
        ans--;
      }
      cout << ans << '\n';
    } else {
      while(ok % A == 0 || ok % B == 0) {
        ok--;
      }
      cout << ans + ok << '\n';
    }
  }
  return 0;
}