#include <bits/stdc++.h>
using namespace std;
#define int long long
signed main(){
	int T;
	cin>>T;
	while(T--){
		int a,b,k;
		cin>>a>>b>>k;
		int t = lcm(a,b);
		int ad = (k/(t-t/a-t/b+1))*t;
		k %= (t-t/a-t/b+1);
		if(k == 0){
			cout<<ad-1<<endl;
			continue;
		}
		int l = 1, r = t;
		while(r-l > 1){
			int md = (l+r)/2;
			if(md-md/a-md/b <= k) l = md;
			else r = md;
		}
		cout<<ad+l<<endl;
	}
}