def gcd(a,b):
	if b==0:
		return a
	return gcd(b,a%b)

def lcm(a,b):
	return (a*b)//gcd(a,b)

for _ in range(int(input())):
    A,B,K=map(int,input().split())
    C=lcm(A,B)
    L,R=0,1<<65
    while R-L>1:
        mid=(L+R)//2
        cnt=mid-(mid//A+mid//B-mid//C)
        if cnt>=K:
            R=mid
        else:
            L=mid
    print(R)