#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=300005,INF=1<<30;

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int Q;cin>>Q;
    while(Q--){
        ll a,b,k;cin>>a>>b>>k;
        ll left=0,right=7e18;
        while(right-left>1){
            ll mid=left+(right-left)/2;
            ll sum=mid;
            sum-=mid/a;
            sum-=mid/b;
            sum+=mid/(a*b/gcd(a,b));
            if(sum>=k) right=mid;
            else left=mid;
        }
        cout<<right<<endl;
    }
}