from math import gcd
import sys
input = sys.stdin.readline

for _ in range(int(input())):
    a, b, k = map(int, input().split())
    lcm_ab = a * b // gcd(a, b)
    l, r = 0, 1 << 63
    while r - l > 1:
        mid = (l + r) // 2
        res = mid - (mid // a + mid // b - mid // lcm_ab)
        if res >= k:
            r = mid
        else:
            l = mid
    print(r)