#include<bits/stdc++.h>
using namespace std;
using ll = long long;


ll gcd(ll a,ll b){
    if(b) return gcd(b,a%b);
    return a;
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    
    int t;
    cin>>t;
    while(t--){
        ll a,b,k;
        cin>>a>>b>>k;
        ll right = 8e18;
        ll left = 0;
        ll g = gcd(a,b);
        g = a / g * b;
        while(right-left>1){
            ll mid = ((right-left)>>1) + left;
            ll cnt = mid / a + mid / b - mid / g;
            if(mid-cnt>=k) right = mid;
            else left = mid;
        }
        cout<<right<<endl;
    }

}