import math
T=int(input())
answers=[]
def solve(A,B,K):
    c=math.lcm(A,B)
    ng=0
    ok=10**19
    while (ok-ng)>1:
        m=(ok+ng)//2
        if(m-(m//B)-(m//A)+(m//c)>=K):
            ok=m
        else:
            ng=m
    return ok
def gutyoku(A,B,K):
    ans=0
    while K>0:
        ans+=1
        if(ans%A==0 or ans%B==0):
            continue
        else:
            K-=1
    return ans

for i in range(T):
    A,B,K=map(int,input().split())
    ans=solve(A,B,K)
    answers.append(ans)
for ans in answers:
    print(ans)