import sys
def gcd(a, b):
	if b == 0:
		return a
	return gcd(b, a % b)
def lcm(a, b):
	return a // gcd(a, b) * b
input = sys.stdin.readline
def solve():
    a, b, k = map(int, input().split())
    ab = lcm(a, b)
    ng, ok = 0, 5 * 10**18
    while ok - ng != 1:
        vs = (ok + ng) >> 1
        gokei = vs - vs // a - vs // b + vs // ab
        if gokei >= k:
            ok = vs
        else:
            ng = vs
    print(ok)
for i in range(int(input())):
    solve()