import math
t=int(input())
for i in range(t):
    a,b,k = map(int,input().split())
    lc = (a*b)//math.gcd(a,b)
    ok = 0
    ng = 2000000000000000000
    while abs(ok-ng)>1:
        mid = (ok+ng)//2
        cna = mid//a
        cnb = mid//b
        cnab = mid//(lc)
        if (mid-(cna+cnb-cnab)<=k):ok=mid
        else:ng = mid
    while ok%a==0 or ok%b==0:ok-=1
    print(ok)