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

ulong gcd(ulong a,ulong b){
	if(!b)return a;
	else return gcd(b,a%b);
}

ulong lcm(ulong a,ulong b){
	return a/gcd(a,b)*b;
}

/*
　l以上r以下の整数で、aまたはbで割り切れる数の個数
 */
ulong count(ulong a, ulong b, ulong l, ulong r){
	ulong g=gcd(a,b); //最大公約数
	ulong m=a/g*b; //最小公倍数
	ulong k=l-1L;
	return (r/a+r/b-r/m)-(k/a+k/b-k/m);
}

ulong solve(ulong a, ulong b, ulong k){
	ulong res=k;
	
	ulong cnt=count(a,b,1L,res);
	while(cnt){
		ulong r=res+1L;
		res+=cnt;
		cnt=count(a,b,r,res);
	}
	return res;

}


int main(){
	int t;
	cin >> t;
	while(t--){
		ulong a,b,k;
		cin >> a >> b >> k;
		cout << solve(a,b,k) << endl;
	}
	return 0;
}