import math
def floor_sum(n, m, a, b):
    ans = 0
    while True:
        if a >= m or a < 0:
            ans += n * (n - 1) * (a // m) // 2
            a %= m
        if b >= m or b < 0:
            ans += n * (b // m)
            b %= m
        y_max = a * n + b
        if y_max < m: break
        n, b, m, a = y_max // m, y_max % m, a, m
    return ans
#sum i=0^n-1 (ai+b)//m

def f(N):
  s=N//P
  a=floor_sum(s+1,Q,-P,N)
  return a+s+1
T=int(input())
for _ in range(T):
  P,Q,K=map(int,input().split())
  K+=1
  #print(f(4))
  g=math.gcd(P,Q)
  P//=g
  Q//=g
  
  sita=0
  ue=P*Q-1
  flag=False
  for i in range(100):
    this=(sita+ue)//2
    if f(this)>=K:
      ue=this
    else:
      sita=this
    if (ue-sita)<=1:
      if f(sita)>=K:
        print(sita*g)
      elif f(ue)>=K:
        print(ue*g)
      else:
        flag=True
        break
      break
  if flag:
    k=f(P*Q-1)
    print((P*Q-1+K-k)*g)