import sys
input = sys.stdin.readline
from math import gcd

def calc(m,a,b,ab):

    return m - m//a - m//b + m//ab
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)
    assert calc(l,a,b,ab) < k
    r = l + 10*ab

    assert calc(r,a,b,ab) > k

    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

    assert calc(l,a,b,ab) == k
    while (l%a == 0) or (l%b == 0):
        l -= 1

    return l

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