#include<iostream>
#include<cassert>
using namespace std;
int gcd(int a,int b)
{
	while(b)
	{
		int t=a%b;
		a=b;
		b=t;
	}
	return a;
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int T;cin>>T;
	for(;T--;)
	{
		int A,B;
		long K;
		cin>>A>>B>>K;
		int g=gcd(A,B);
		long lcm=(long)A/g*B;
		long L=0,R=4e18;
		while(R-L>1)
		{
			long M=(L+R)/2;
			if(M-(M/A+M/B-M/lcm)>=K)R=M;
			else L=M;
		}
		cout<<R<<"\n";
	}
}