I=input
for t in range(int(I())):
	A,B,K=map(int,I().split())
	C,D=A,B
	if A>B:C,D=D,C
	while C:C,D=D%C,C
	C=A*B//D
	N=int((K+1)/(1-1/A-1/B+1/C))
	while N-N//A-N//B+N//C>=K:N-=1
	while N-N//A-N//B+N//C<K:N+=1
	print(N)