import sys
from math import lcm


input = sys.stdin.readline


def main():
    A, B, K = map(int, input().split())
    L = lcm(A, B)
    ok, ng = (1 << 80), 0
    while ok - ng > 1:
        mid = (ok + ng) // 2
        if mid - (mid // A) - (mid // B) + (mid // L) >= K:
            ok = mid
        else:
            ng = mid
    
    print(ok)

if __name__ == '__main__':
    T = int(input())
    for _ in range(T):
        main()