// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <complex>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#include <vector>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#define TEST cerr << "TEST" << endl
#define AMARI 998244353
// #define AMARI 1000000007
#define TIME_LIMIT 1980000
#define el '\n'
#define El '\n'

long long ococo_gcd(long long a, long long b) {
    if(a < b) {
        swap(a,b);
    }
    if(b == 0 && a != 0)return a;
    long long ans = a;
    while(a % b) {
        long long kari = b;
        b = a % b;
        a = kari;
    }
    return min(a, b);
}

ll lcm(ll a,ll b){
    return (a * b) / ococo_gcd(a,b);
}
//[1,x]の中で、pまたはqで割り切れる数がa個以上かどうか lmはlcm(p,q)を入れる
bool func(ll x,ll p,ll q,ll lm,ll a){
    ll cnt1 = x - x / p,cnt2 = x - x / q,cnt3 = x - x / lm;
    if(cnt1 + cnt2 - cnt3 >= a)return true;
    else return false;
}

#define MULTI_TEST_CASE true
void solve(void) {
    ll a,b,k;
    cin >> a >> b >> k;
    ll lm = lcm(a,b);
    ll l = 0,r = 4LL * k;
    while(r - l >= 2){
        ll c = (r + l) / 2;
        if(func(c,a,b,lm,k))r = c;
        else l = c;
    }
    for(ll i = l; i <= r; i++){
        if(func(i,a,b,lm,k)){
            cout << i << el;
            return;
        }
    }
    assert(0);
    return;
}

void calc(void) {
    return;
}

signed main(void) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    calc();
    int t = 1;
    if(MULTI_TEST_CASE) cin >> t;
    while(t--) {
        solve();
    }
    return 0;
}