Final answer:
The least upper bound of 8 and 12 in the given set is 24, as this is the smallest number that both can divide into without any remainder.
Step-by-step explanation:
The least upper bound (LUB) in a divisibility relation is the smallest common divisor that all elements in the set can divide into without any remainder. For the elements 8 and 12, the least upper bound within the given set (1, 2, 3, 6, 8, 12, 24, 36) would be the smallest number that both can divide into exactly. Considering the set, 24 is divisible by both 8 and 12, and there are no smaller numbers in the set that both 8 and 12 can divide into. Therefore, the least upper bound of 8 and 12, within the context of this set, is 24.