import math
import sys
input = sys.stdin.readline
T = int(input())
ABK = [list(map(int, input().split())) for _ in range(T)]
for a, b, k in ABK:
    g = math.gcd(a, b)
    l = a//g*b

    left = 0
    right = 10**19
    while right-left>1:
        mid = (left+right)//2
        cnt = mid//a + mid//b - mid//(l)
        if mid-cnt>=k:
            right = mid
        else:
            left = mid
    print(right)