import sys
input = sys.stdin.readline
from math import gcd
def solve():

    a,b,k = map(int,input().split())
    ab = a*b//(gcd(a,b))

    base = ab - ab//a - ab//b + 1

    l = max((k-1)//base * ab-ab,0)
    r = l + 2*ab

    while r - l > 1:

        m = (r+l)//2

        num = m

        num -= m//a + m//b
        num += m//ab

        if num > k:
            r = m
        else:
            l = m

    return l

t = int(input())
for _ in range(t):
    print(solve())