The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
+6 votes

Consider the set of integers $\{1,2,3,4,6,8,12,24\}$ together with the two binary operations LCM (lowest common multiple) and GCD (greatest common divisor). Which of the following algebraic structures does this represent?

  1. group
  2. ring
  3. field
  4. lattice
asked in Set Theory & Algebra by Veteran (99.2k points) | 318 views

1 Answer

+8 votes
Best answer

ans is lattice .



answered by Veteran (55.6k points)
selected by
How did you draw this lattice? How two elements are related?
I think this lattice has been drawn like this:

For any two elements a and b in this lattice, if a < b then b is the LCM of a and b and a is the GCD of a and b. For example, if 1 and 3 are connected then 3 is the LCM of 1 and 3 and 1 is the GCD of 1 and 3.

This is lattice (D24,|)  over partial order relation divisibility. Where D24 indicates positive integral divisors of 24.

LCM is given by LUB and HCF is given by GLB.


how can we have two operations in a lattice?

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

29,138 questions
36,958 answers
34,802 users