from math import lcm

def cnt_indivisible(n):
	return n - n//A - n//B + n//L
	
for _ in range(T := int(input())):
  A, B, K = map(int, input().split())
  L = lcm(A, B)
  
  ng, ok = 0, 10**19
  while ok - ng > 1:
  	md = (ng + ok)//2
  	if cnt_indivisible(md) >= K:
  		ok = md
  	else:
  		ng = md
  
  print(ok)