#include <stdio.h>
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf32 1000000001
#define Inf64 1000000000000000001

int main(){
	
	int _t;
	cin>>_t;
	
	rep(_,_t){
		long long a,b,k;
		cin>>a>>b>>k;
		
		long long ok = 0,ng = k*3 + k + k + k;
		while(ng-ok>1LL){
			long long mid = (ok+ng)/2;
			long long t = mid/a;
			t += mid/b;
			t -= mid/lcm(a,b);
			t = mid-t;
			if(t<=k-1)ok = mid;
			else ng = mid;
			
		}
		cout<<ok+1<<endl;
	}
	
	return 0;
}