Lattice

https://en.wikipedia.org/wiki/Lattice_(order)

A lattice is an abstract structure consisting of a poset in which every two elements have a unique supremum (least upper bound or join) and a unique infimum (greatest lower bound or meet). An example is given by the natural numbers, partially ordered by divisibility, for which the unique supremum is the least common multiple and the unique infimum is the greatest common divisor.

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

A lattice consists of a partially ordered set in which every two elements have a unique supremum (least upper bound or join) and a unique infimum (greatest lower bound or meet).

An example is given by the natural numbers, partially ordered by divisibility, for which the unique supremum is the least common multiple (LCM) and the unique infimum is the greatest common divisor (GCD).

1 2 2 1 2 4 2 2 3 4 4 2 2 6 1 2 2 4 6 ↓ ↓ ↓ ↓ ↓ ↓

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30	D
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1	1
2 2 2 2 2 2 3 2 2 2 2 2 2 2 2	2
3 3 3 3 3 3 3 3	3
4 4 4 4 4 4 4	4
5 5 5 5 5 ⅙ 5	5
6 6 6 6 ⅕ 6	6
7 7 7 ¼ 7	7
⅟ 8 ½ 8 ⅓ 8	8
9 9 9	9
10 10 10	10
11 11	11
12 12	12
13 13	13
14 14	14
15 15	15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30	n