from math import gcd
import sys

input = sys.stdin.readline

t = int(input())
for _ in range(t):
	ai, bi, ki = [int(x) for x in input().split()]
	li = ai // gcd(ai, bi) * bi
	ui = li - li // ai - li // bi + 1
	pi = (ki + ui - 1) // ui
	left = li * (pi - 1)
	right = li * pi + 1
	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)