from sys import stdin
import math
def input(): return stdin.readline()


def main():
    T = int(input())
    for _ in range(T):
        a, b, k = map(int, input().split())
        l = 1
        r = 3 * 10**18
        while l < r:
            mid = l + (r - l) // 2
            count = mid - mid // a - mid // b + mid // (a * b // math.gcd(a, b))
            if count < k:
                l = mid + 1
            else:
                r = mid
        print(l)

if __name__ == "__main__":
    main()