#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic warning "-Wunused-function"
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  using ull = unsigned long long;
  int tt;
  cin >> tt;
  while(tt--) {
    ull a, b, k;
    cin >> a >> b >> k;
    k--;
    auto ab = lcm(a, b);
    ull l = 0, r = 5e18;
    while(r - l > 1) {
      ull c = (l + r) / 2;
      auto cnt = c - c / a - c / b + c / ab;
      (cnt > k ? r : l) = c;
    }
    cout << r << '\n';
  }
}