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
	L,R=1,2**62
	while L<R:
		M=(L+R)//2
		if M-M//A-M//B+M//C<K:L=M+1
		else:R=M
	print(L)