#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i,m,n) for(int i=m; i<int(n); ++i)
#define repll(i,m,n) for(ll i=m; i<ll(n); ++i)
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define fi first
#define se second

template<typename T> bool chmin(T& a, T b){ if(a > b){a = b; return true;} return false; }
template<typename T> bool chmax(T& a, T b){ if(a < b){a = b; return true;} return false; }

template<typename T> T gcd(T a, T b){ return a % b ? gcd(b, a % b) : b; }
template<typename T> T lcm(T a, T b){ return a / gcd(a, b) * b; }

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

    int T;
    cin >> T;

    while(T--){
        ll A, B, K;
        cin >> A >> B >> K;

        ll lo = 0LL, hi = 1LL << 62, mid, x;
        while(abs(lo - hi) > 1LL){
            mid = (lo + hi) / 2LL;

            x = mid - (mid / A + mid / B - mid / lcm(A, B));
            (x >= K ? hi : lo) = mid;
        }
        cout << hi << endl;
    }

    return 0;
}