import math
t = int(input())
for _ in range(t):
	a, b, k = map(int, input().split())
	l = math.lcm(a, b)
	lo, hi = 0, 2 * 10 ** 18
	while lo + 1 < hi:
		mid = (lo + hi) // 2
		cnt = mid - mid // a - mid // b + mid // l
		if cnt >= k:
			hi = mid
		else:
			lo = mid
	print(hi)