#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;
using ll = long long;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using VD = vector<double>;
using VVD = vector<VD>;
using VS = vector<string>;
using P = pair<ll,ll>;
using VP = vector<P>;
#define rep(i, n) for (ll i = 0; i < ll(n); i++)
#define out(x) cout << x << endl
#define dout(x) cout << fixed << setprecision(10) << x << endl
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define sz(x) (int)(x.size())
#define re0 return 0
#define pcnt __builtin_popcountll
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
constexpr int inf = 1e9;
constexpr ll INF = 1e18;
//using mint = modint1000000007;
using mint = modint998244353;
int di[4] = {1,0,-1,0};
int dj[4] = {0,1,0,-1};

void solve(){
    ll a,b,k;
    cin >> a >> b >> k;
    ll ok = 0,ng = LLONG_MAX;
    auto f = [&](ll x){
        ll res = x;
        res -= x/a;
        res -= x/b;
        res += x/lcm(a,b);
        return res;
    };
    while(abs(ok-ng)>1){
        ll mid = (ok+ng)/2;
        if(f(mid) <= k) ok = mid;
        else ng = mid;
    }    
    out(ok);
}

int main(){
    int t;
    cin >> t;
    rep(ti,t) solve();
}