T=int(input())
def gcd(x, y): 
    if y == 0: 
        return x 
    else: 
        return gcd(y, x % y) 
      
for _ in range(T):
  a,b,k=map(int, input().split())
  c=a*b//gcd(a,b)
  ok,ng=0,10**20+1
  while (ng-ok)>1:
    mid=(ok+ng)//2
    d=mid-mid//a-mid//b+mid//c
    if d>=k:
      ng=mid 
    else:
      ok=mid 
  print(ng)