import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return list(map(int, input().split()))
sys.setrecursionlimit(10**9)

from math import gcd
T = int(input())
for _ in range(T):
    A, B, K = mapint()
    lc = A*B//gcd(A, B)
    l = 0
    r = 10**18 * 20
    while l+1<r:
        tar = (l+r)//2
        cnt = tar - tar//A - tar//B + tar//lc
        if(cnt >= K):
            r = tar
        else:
            l = tar
    print(r)