from collections import *
from functools import *
from itertools import *
from heapq import *
import sys,math
input = sys.stdin.buffer.readline
# sys.maxsize = (1<<64) - 1
def answer():
    A,B,K = map(int,input().split())
    
    def is_ok(x):
        
        tmp = (x//A) + (x//B) - (x//(A*B//math.gcd(A,B)))
        
        return x-tmp >= K
        
    y = min((1<<62),K*A*B)
    x = K-1
    while y-x>1:
        mid = (y+x)//2
        if is_ok(mid):
            y = mid
        else:
            x = mid
    print(y)
for _ in range(int(input())):
    answer()