+434 Let $S$ be the set of numbers of the form
n(n + 1)(n + 3)(n + 4)(n + 8)(n + 10)(n + 12)
where $n$ is any positive integer.
What is the GCD of the elements of $S$?
+135 It could have no multiple of 7: (15, 16, 18, 20, 22, 24, 26)
It must have at least 1 multiple of 5: (8, 9, 11, 13, 15, 17, 19)
It must have at least 2 multiples of 3: (13, 14, 15, 17, 19, 21, 23, 25)
It must have at least 1 multiple of 2: (2, 3, 5, 7, 9, 11, 13, 15)
Therefore the GCF is 5 * 3 * 3 * 2 = 90
