import math
T = int(input())
for _ in range(T) :
	a, b, k = map(int, input().split())
	L = math.lcm(a, b)
	num = L - (L // a) - (L // b) + 1
	k -= 1
	ans1 = k // num
	k %= num
	k += 1
	ok = L - 1
	ng = 0
	while abs(ok - ng) > 1 :
		md = (ok + ng) // 2
		nn = (md + 1) - (md // a + 1) - (md // b + 1) + 1
		if nn >= k :
			ok = md
		else :
			ng = md
	# print(f"L : {L}, num : {num}, ans1 : {ans1}, ok : {ok}")
	print(ans1 * L + ok)