#include <bits/stdc++.h>
using namespace std;
using ll = long long;
void solve(){
    ll A,B,K;
    cin>>A>>B>>K;
    ll G=A/gcd(A,B)*B,L=0,R=4e18;
    while(R-L>1){
        ll M=(R+L)/2,a=(M/A)+(M/B)-(M/G);
        (M-a<=K?L:R)=M;
    }
    cout<<L<<endl;
}

int main() {
    ll T;
    cin>>T;
    while(T--)solve();
}