#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using pll = pair<ll, ll>;
#define drep(i, cc, n) for (ll i = (cc); i <= (n); ++i)
#define rep(i, n) drep(i, 0, n - 1)
#define all(a) (a).begin(), (a).end()
#define pb push_back
#define fi first
#define se second
mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count());
const ll MOD1000000007 = 1000000007;
const ll MOD998244353 = 998244353;
const ll MOD[3] = {999727999, 1070777777, 1000000007};
const ll LINF = 1LL << 60LL;
const int IINF = (1 << 30) - 1;


template<typename T>
struct edge{
    int from, to;
    T cost;

    edge(){}
    edge(int to, T cost = 1) : from(-1), to(to), cost(cost){}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost){}
};

template<typename T>
struct redge{
    int from, to;
    T cap, cost;
    int rev;
    
    redge(int to, T cap, T cost=(T)(1)) : from(-1), to(to), cap(cap), cost(cost){}
    redge(int to, T cap, T cost, int rev) : from(-1), to(to), cap(cap), cost(cost), rev(rev){}
};

template<typename T> using Edges = vector<edge<T>>;
template<typename T> using weighted_graph = vector<Edges<T>>;
template<typename T> using tree = vector<Edges<T>>;
using unweighted_graph = vector<vector<int>>;
template<typename T> using residual_graph = vector<vector<redge<T>>>;


using l3 = __int128_t;

void solve(){
    ll tmp_a, tmp_b, tmp_k;
    cin >> tmp_a >> tmp_b >> tmp_k;
    ll tmp_l = tmp_a*tmp_b/__gcd(tmp_a, tmp_b);

    l3 a = (l3)tmp_a, b = (l3)tmp_b, k = (l3)tmp_k;
    l3 l = (l3)tmp_l;

    l3 lo = 1;
    l3 hi = (l3)1e20;
    l3 mid;
    while(hi-lo>1){
        mid = (lo + hi)/2;
        l3 cnt = mid/a + mid/b - mid/l;
        if(mid-cnt<=k) lo = mid;
        else hi = mid;
    }

    ll ans = (ll)lo;
    cout << ans << '\n';
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    
    int T=1;
    cin >> T;
    while(T--) solve();
}