#include <iostream>
#include <numeric>
using namespace std;

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    int T;
    cin >> T;
    while (T--) {
        long long A, B, K;
        cin >> A >> B >> K;
        const auto l = std::lcm(A, B);

        long long ng = K - 1, ok = 1LL << 62;
        while (ok - ng > 1) {
            const auto mid = (ok + ng) / 2;

            auto nin = mid - mid / A - mid / B + mid / l;

            if (nin >= K) {
                ok = mid;
            } else {
                ng = mid;
            }
        }
        cout << ok << '\n';
    }
}