#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>
#include <atcoder/math>

#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;

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; }

using namespace std;
typedef long long ll;

template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
    return vector<vector<T>>(n, vector<T>(m, v));
}

template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
    return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}

template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
    if(v.empty()) {
        cout << endl;
        return;
    }
    for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
    cout << v.back() << endl;
}


/**
 * ax + by = gcd(a, b)を満たす(x, y)をつめて、gcd(a, b)を返します。
 */ 
template <typename T>
T extGCD(T a, T b, T &x, T &y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    T d = extGCD(b, a%b, y, x);
    y -= a/b * x;
    return d;
}


// calc ceil(a/b) 
template<typename T>
T ceil_div(T a, T b){
    return (a+b-1)/b;
}

void solve(){
    ll p, q, k; cin >> p >> q >> k;
    if(p == q){
        cout << p*k << endl;
        return;
    }
    if(p > q) swap(p, q);
    ll a, b;
    extGCD(p, q, a, b);
    if(a < 0){
        ll x = ceil_div(-a, q);
        a += x*q;
        b -= x*p;
    }
    if(a > q){
        ll x = a/q;
        a -= x*q;
        b += x*p;
    }
    b *= -1;
    ll g = gcd(p, q);
    p /= g;
    q /= g;
    function<ll(ll)> count = [&](ll x){
        if(x >= p*q){
            return count(p*q-1)+x-p*q+1;
        }
        ll upper = atcoder::floor_sum(x+1, q, a, 0);
        ll lower = atcoder::floor_sum(x+1, p, b, 0);
        ll on_line = x/p;
        return upper-lower+on_line;
    };
    ll l = 0, r = p*q+k;
    while(r-l > 1){
        ll x = (l+r)/2;
        if(count(x) >= k) r = x;
        else l = x;
    }
    cout << r*g << endl;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int t; cin >> t;
    while(t--) solve();
}