import math
t = int(input())

def check(mid, r, a, b):
    if mid - (mid // a + mid // b) >= r:
        return True
    return False

for _ in range(t):
    a, b, k = map(int, input().split())
    lcm = a * b // math.gcd(a, b)
    wareru = lcm // a + lcm // b - 1
    d, r = divmod(k, lcm - wareru)
    mn = 0
    mx = lcm
    while mx - mn > 1:
        mid = (mx + mn) // 2
        if check(mid, r, a, b): # midは小さい方からr番目以上
            mx = mid
        else:
            mn = mid
        
    print(d * lcm + mx)