A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
what is an alternative definition for least common multiple besides min{m : am and bm} ?
anonymous
 one year ago
what is an alternative definition for least common multiple besides min{m : am and bm} ?

This Question is Closed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1I think that definition is the most intuitive one as it simply says what the name "least common multiple" means

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1for two integers \(a,b\) we do have this relationship though : \[\text{lcm}(a,b) = \dfrac{ab}{\gcd(a,b)}\] but that doesn't work for more than two integers

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, but It has no arithmetic structure. I was looking for something like i) m > 0 ii) am and bm ...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and that's actually a theorem. I'm looking for a definition though

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1right, when you do prime factorization, that definition plays very nicely, you can play with the exponents

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1that same definition can be expressed as below : \(\text{lcm}(a,b)\) is the positive integer \(m\) satisfying : 1) \(a\mid m\) and \(b\mid m\) 2) \(a\mid c\) and \(b\mid c\) \(\implies\) \(m\le c\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1I don't see how that definition is any inferior to the definition of \(\gcd\) what arithmetic structure do you have in mind ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0actually, that's exactly what i was looking for. Some sort of criteria that a least common multiple must follow

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1ohk.. but yes that definition is pretty useless when prime factorization is not possible

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh... I think it's still better than min{m : am and bm}

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1both are same, aren't they..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0they are indeed. I just prefer the one that is formally written out.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.