"""

https://yukicoder.me/problems/no/2526



"""

import math
import sys
from sys import stdin

TT = int(stdin.readline())

ANS = []

for loop in range(TT):

    A,B,K = map(int,stdin.readline().split())
    lcm = A*B // math.gcd(A,B)

    L = -1
    R = 10**19

    while R-L != 1:

        M = (L+R)//2

        now = M
        now -= M // A
        now -= M // B
        now += M // lcm

        if now >= K:
            R = M
        else:
            L = M

    ANS.append(R)

print (*ANS,sep="\n")