import sys
input = sys.stdin.readline
from math import lcm

T=int(input())
for tests in range(T):
    A,B,K=map(int,input().split())
    LCM=lcm(A,B)
    # 1～LCM中に、LCM/A+LCM/B-1個が条件を満たさない

    k=LCM//A+LCM//B-1
    #print(LCM,k)
    rest=LCM-k

    x=K//rest
    ANS=x*LCM
    K-=rest*x

    #print(ANS,K)

    if K==0:
        print(ANS-1)
        continue

    OK=LCM
    NG=0

    while OK>NG+1:
        mid=(OK+NG)//2

        if mid-(mid//A)-(mid//B)>=K:
            OK=mid
        else:
            NG=mid

    print(ANS+OK)