import collections,sys,math,functools,operator,itertools,bisect,heapq,decimal,string,time,random
#sys.setrecursionlimit(10**9)
input = sys.stdin.readline

def solve():
    a,b,k = map(int,input().split())
    c = a*b//math.gcd(a,b)
    l,r = 0,10**20
    while r-l > 1:
        m = (l+r)//2
        cnt = m // a + m // b - m // c
        if m - cnt >= k:
            r = m
        else:
            l = m
    print(r)

for _ in range(int(input())):
    solve()