#include <bits/stdc++.h>
using namespace std;

int main() {
  int t; cin >> t;
  for(int T=0;T<t;T++){
    long long a, b, k; cin >> a >> b >> k;
    long long ans = k, L = lcm(a,b);
    while(ans - ans/a - ans/b + ans/L != k){
      ans += k - (ans - (ans/a + ans/b - ans/L));
    }
    cout << ans << endl;
  }
}