#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using ll = long long;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
using mint = atcoder::modint998244353;

ll gcd(ll a,ll b){
	if(b==0) return a;
	return gcd(b,a%b);
}

int main(){
	int t;
	cin>>t;
	rep(Ti,t){
		ll a,b,k;
		cin>>a>>b>>k;
		ll l=a/gcd(a,b)*b;
		ll up=5e18;
		ll dw=0;
		while(up-dw>1){
			ll md=(up+dw)/2;
			ll ct=0;
			ct+=md/a;
			ct+=md/b;
			ct-=md/l;
			if(md-ct>=k) up=md;
			else dw=md;
		}
		cout<<up<<"\n";
	}
}