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

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int T;
    cin >> T;
    while(T--){
        ll a, b, k;
        cin >> a >> b >> k;
        ll ng = 0, ok = (1ll << 61) - 1 + (1ll << 61), mid;
        auto f = [&](ll v){
            ll res = v;
            res -= v / a + v / b;
            res += v / lcm(a, b);
            return res;
        };
        while(ng + 1 < ok){
            mid = (ok + ng) / 2;
            (f(mid) >= k ? ok : ng) = mid;
        }
        cout << ok << '\n';
    }
}