# 二分探索と包除原理だな
# ポラード・ロー素因数分解法でもTLE

from math import lcm

def check(X):
    divisible = 0
    divisible += X//A
    divisible += X//B
    divisible -= X//AB
    if X-divisible<K:
        return 0
    else:
        return 1

T = int(input())
for t in range(T):
    A, B, K = map(int, input().split())
    AB = lcm(A, B)

    NG = 0
    OK = K*2+2
    while (OK-NG)>1:
        mid = (OK+NG)//2
        if check(mid)==1:
            OK=mid
        else:
            NG=mid
    print(OK)