import math
def isok(n):
    ans=n-n//A-n//B+n//math.lcm(A,B)
    if ans<K:
        return True
    return False

T=int(input())
for _ in range(T):
    A,B,K=map(int,input().split())
    left,right=0,3*10**18+1
    while right-left>1:
        mid=(right+left)//2
        if isok(mid):
            left=mid
        else:
            right=mid
    print(right)