from math import gcd
t = int(input())
for _ in range(t):
	ai, bi, ki = [int(x) for x in input().split()]
	li = ai // gcd(ai, bi) * bi
	left = 0
	right = li * ki
	while right - left > 1:
		mid = (right + left) // 2
		x = mid - (mid // ai) - (mid // bi) + (mid // li)
		if x >= ki:
			right = mid
		else:
			left = mid
	print(right)