#include<bits/stdc++.h>
using namespace std;
template<typename T>
T gcd(T a, T b){return b==0?a:gcd(b,a%b);}
template<typename T>
T lcm(T a, T b){return a/gcd(a,b)*b;}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int T;
    cin>>T;
    while(T--)
    {
        long A,B,K;
        cin>>A>>B>>K;
        long C=lcm(A,B);
        long L=0,R=3e18;
        while(R-L>1)
        {
            long mid=(L+R)/2;
            long cnt=mid-(mid/A+mid/B-mid/C);
            (cnt>=K?R:L)=mid;
        }
        cout<<R<<'\n';
    }
}