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

    lb = K
    ub = K * 10

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