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

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int test; cin >> test;
    while(test--){
        long long A,B,K; cin >> A >> B >> K;
        if(A > B) swap(A,B);
        long long G = gcd(A,B),L = A*B/G;
        long long loop = L-(L/A+L/B-1);
        long long answer = L*(K/loop);
        K %= loop;

        long long low = -1,high = L-1;
        while(high-low > 1){
            long long mid = (high+low)/2;
            long long now = mid-(mid/A+mid/B);
            if(now >= K) high = mid;
            else low = mid;
        }
        cout << answer+high << endl;
    }
}