t=int(input())
import math
for _ in range(t):
  a,b,k=map(int,input().split())
  g=math.gcd(a,b)
  c=(a*b)//g
  l=50
  m=int(k*a*b*c/(a*b*c-a*c-b*c+a*b))
  for i in range(max(1,m-l),m+l):
    if i-(i//a+i//b-i//((a*b)//g))==k:
      print(i)
      break