import math

def LCM(n,m):
    if n or m:
        return abs(n)*abs(m)//math.gcd(n,m)
    return 0

def Bisect_Int(ok,ng,is_ok):
    while abs(ok-ng)>1:
        mid=(ok+ng)//2
        if is_ok(mid):
            ok=mid
        else:
            ng=mid
    return ok

T=int(input())
for t in range(T):
    A,B,K=map(int,input().split())
    lcm=LCM(A,B)
    def is_ok(x):
        return x-1-(x-1)//A-(x-1)//B+(x-1)//lcm<K
    ans=Bisect_Int(1,K*3+3,is_ok)
    print(ans)