import sys
sys.setrecursionlimit(5*10**5)
input = sys.stdin.readline
from collections import defaultdict, deque, Counter
from heapq import heappop, heappush
from bisect import bisect_left, bisect_right
from math import gcd

def sol():
    a,b,k = map(int,input().split())
    ab = a*b//gcd(a,b)
    l = 0
    r = 2*10**18
    for i in range(70):
        m = (l+r)//2
        cnt = m-m//a-m//b+m//ab
        if cnt <= k:
            l = m
        else:
            r = m
    print(*[l])
    return 


T = int(input())
for i in range(T):
    sol()