import math
T=int(input())
answers=[]
for i in range(T):
    A,B,K=map(int,input().split())
    c=math.lcm(A,B)
    s=c-(c//A-1)-(c//B-1)-1
    ans=0
    ans+=(K//s)*c
    K=K%s
    ok=c
    ng=0
    while (ok-ng)>1:
        m=(ok+ng)//2
        if(m-m//A-m//B>=K):
            ok=m
        else:
            ng=m
    ans+=ok
    answers.append(ans)
for ans in answers:
    print(ans)