wu :: forums
« wu :: forums - LCM »

Welcome, Guest. Please Login or Register.
Mar 28th, 2024, 3:07pm

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   medium
(Moderators: Icarus, towr, Eigenray, william wu, ThudnBlunder, SMQ, Grimbal)
   LCM
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: LCM  (Read 628 times)
Christine
Full Member
***





   


Posts: 159
LCM  
« on: Jun 7th, 2015, 2:51pm »
Quote Quote Modify Modify

What is the LCM of  sqrt(2) and sqrt(3) ?
 
I was told to use continued fractions, but I don't know how to do it. Help!
« Last Edit: Jun 7th, 2015, 2:52pm by Christine » IP Logged
pex
Uberpuzzler
*****





   


Gender: male
Posts: 880
Re: LCM  
« Reply #1 on: Jun 7th, 2015, 5:21pm »
Quote Quote Modify Modify

on Jun 7th, 2015, 2:51pm, Christine wrote:
What is the LCM of  sqrt(2) and sqrt(3) ?

Is this even well-defined? Assuming LCM is least common multiple, which is commonly defined for integers only. I can see how to extend the concept to rationals, but for irrational numbers...
 
I suppose a common multiple would be a positive number m such that m = a*sqrt(2) = b*sqrt(3). What are a and b allowed to be? Clearly they can't both be integers, since sqrt(2/3) is irrational. But if they're not integers, nothing prevents us from replacing them by m/2 = (a/2)sqrt(2) = (b/2)sqrt(3) and no least common multiple exists.
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: LCM  
« Reply #2 on: Jun 7th, 2015, 10:28pm »
Quote Quote Modify Modify

Perhaps we need to find some approximate LCM, within a certain tolerance. Like: m = a*2 = b*3 with |a*2 - [a*2| < 0.01 and |b*3 - [b*3]| < 0.01, and a,b,m integers
 
So, for example  
9513*3 = 16476.9993
11651*2 = 16477.0022
So, 16477 might be considered the LCM for 2 and 3 with a given tolerance.
 
 
[edit]
Or perhaps it's simpler to consider: |m - a*2| < t and |m - b*3| < t, and a, b, m integers and some tolerance t
e.g m=134421, a=95050, b=77608, t~=0.0021
[/edit]
« Last Edit: Jun 7th, 2015, 11:07pm by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
pex
Uberpuzzler
*****





   


Gender: male
Posts: 880
Re: LCM  
« Reply #3 on: Jun 7th, 2015, 11:00pm »
Quote Quote Modify Modify

... and good rational approximations of irrational numbers are commonly found using continued fractions, so using towr's interpretation, the hint actually makes sense. Good mind reading! Smiley
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: LCM  
« Reply #4 on: Jun 7th, 2015, 11:17pm »
Quote Quote Modify Modify

Quote:
Good mind reading!
It helped that I googled a bit, I found this, for example.
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board