from math import gcd
for _ in range(int(input())):
	a, b, k = map(int, input().split())
	g = gcd(a, b)
	l = a // g * b
	le = 1
	ri = 10 ** 20
	while le + 1 < ri:
		mi = (le + ri) // 2
		if mi - ((mi // a) + (mi // b) - (mi // l)) > k:
			ri = mi
		else:
			le = mi
	print(le)