def gcd(a,b):
    if b==0:
        return a
    return gcd(b,a%b)
T = int(input())
for _ in range(T):
    a,b,k = map(int,input().split())
    d = gcd(a,b)
    m = a*b//d
    high = 10**19
    low = 0
    while high-low>1:
        mid = (high+low)//2
        cnt = mid//a+mid//b-mid//m
        cnt = mid-cnt
        if cnt>=k:
            high = mid
        else:
            low = mid
    print(high)