from math import*
t=int(input())
def judge(x,a,b,l,k):
  x+=x//l-x//a-x//b
  return k<=x
for _ in range(t):
  a,b,k=map(int,input().split())
  l=a*b//gcd(a,b)
  ok,ng=10**20,0
  while abs(ok-ng)>1:
    mid=ok+ng>>1
    if judge(mid,a,b,l,k):
      ok=mid
    else:
      ng=mid
  print(ok)