from math import lcm

for _ in range(int(input())):
    A,B,K = map(int,input().split())
    C = lcm(A,B)

    lb = 0
    ub = K * 10

    while ub - lb > 1:
        mid = (ub + lb) // 2
        if mid - mid//A - mid//B + mid//C >= K:
            ub = mid
        else:
            lb = mid
    while ub % A == 0 or ub % B == 0:
        ub -= 1
    print(ub)