#include <bits/stdc++.h>
#include <atcoder/all>
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP1(i,n) for (auto i = std::decay_t<decltype(n)>{}; (i) != (n); ++(i))
#define REP2(i,l,r) for (auto i = (l); (i) != (r); ++(i))
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
using namespace std;
using namespace atcoder;
using ll = long long;
using ull = unsigned long long;
using P = pair<int,int>;
using LP = pair<long long,long long>;
using SP = pair<string,string>;
using vi = vector<int>;
using vl = vector<long long>;
using vs = vector<string>;
using vc = vector<char>;
using mint1 = modint1000000007;
using mint9 = modint998244353;
const int INF = 2e9;
const long long LINF = 4e18;
const int di[] = {0,1,0,-1,-1,1,-1,1};
const int dj[] = {1,0,-1,0,1,1,-1,-1};
template<class T> inline bool chmin(T& a, T b){if(a>b){a=b;return true;}return false;}
template<class T> inline bool chmax(T& a, T b){if(a<b){a=b;return true;}return false;}
void YesNo (bool ok , const string &s , const string &t) {if(ok) cout << s << endl; else cout << t << endl;} 


//-----def end-----//

long long f (long long x , long long a , long long b) {
    return x-x/a-x/b+x/lcm(a,b);
}

void solve () {
    long long a , b , k;
    cin >> a >> b >> k;
    long long l = 0 , r = 4e18;
    while (r-l>1) {
        long long mid = (l+r)/2;
        if(k < f(mid,a,b)) r = mid;
        else l = mid;
    }
    for(long long i = -10; i <= 10; i++) {
        if(l+i<0) continue;
        if(f(l+i,a,b) == k && (l+i)%a && (l+i)%b) {
            cout << (l+i) << endl;
            return;
        }
    }
}

int main () {
    int t;
    cin >> t;
    rep(ti , t) solve();
	return 0;
}