Least common multiple and fraction learning ? - Mothering Forums

Forum Jump: 
 
Thread Tools
#1 of 3 Old 07-25-2012, 07:31 AM - Thread Starter
 
Kimcarrots's Avatar
 
Join Date: May 2004
Location: noho ma
Posts: 277
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)

Hello,

 

I need help with the concept of least common multiple(s) with our Singapore math work.

 

I just go up the multiples in my head until I find one in common with both denominators - but I suspect  orngbiggrin.gif  that some of you sassy ladies have a better way.

 

Educate me please! 

Kimcarrots is offline  
#2 of 3 Old 07-25-2012, 08:23 AM
 
moominmamma's Avatar
 
Join Date: Jul 2003
Location: In the middle of nowhere, at the centre of everything.
Posts: 5,690
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 65 Post(s)

There's a lovely little algorithm that's taught in some of the Singapore programs. You start by putting the two numbers at the top of two columns. Then you factor them both, creating columns as you go. For instance, as a first step you might recognize that 3 goes into both 24 and 18, so write it in a left-most column:

 

 

   | 24 |  18  

3  |    |    

 

And then factor out the numbers and write the answers:

 

   | 24 |  18  

3  |  8 |   6

 

 

Carry on. You'll see that 2 goes into both 8 and 6, so do that next: 

 

   | 24 |  18  

3  |  8 |   6

2  |  4 |   3

 

Sometimes you can only factor one of the two numbers in a given row. For instance, the 4 above can be factored by 2, but the 3 can't be. So you just leave the 3, carrying it down to the next row.

 

   | 24 | 18  

3  |  8 |  6

2  |  4 |  3

2  |  2 |  3
 

 

And you just carrying on, factoring one or both columns a row at a time until you have both factored down to 1. So you can put one 2 into 2, carrying the 3 down. And then you can put one 3 into the 3.

 

   | 24 | 18  

3  |  8 |  6

2  |  4 |  3

2  |  2 |  3

2  |  1 |  3

3  |  1 |  1

 

Once you've worked both your starting numbers down to 1's, you're done with the factoring. Your Lowest Common Multiple is all the factors in the left-most column multiplied together: 3 x 2 x 2 x 2 x 3 = 72.

 

You don't necessarily need to use prime factors. For instance, you might have noticed that 6 goes into both numbers at the beginning, and then you could have factored 4 into the 4, rather than putting 2 in twice: 

 

   | 24 | 18  

6  |  4 |  3

4  |  1 |  3

3  |  1 |  3

 

You end up with the same result (6 x 4 x 3 = 72). 

 

The whole process seems a little unwieldy with smallish numbers, but with larger numbers (say, 84 and 294) it figures out LCMs you can't easily do in your head. 

 

Miranda


Mountain mama to three great kids and one great grown-up

moominmamma is online now  
#3 of 3 Old 07-25-2012, 08:30 AM - Thread Starter
 
Kimcarrots's Avatar
 
Join Date: May 2004
Location: noho ma
Posts: 277
Mentioned: 0 Post(s)
Tagged: 0 Thread(s)
Quoted: 0 Post(s)

Wow Miranda - you are like my "Shell Answer Man" lately....(remember him?)... can you move into my house?  I have a cute baby to snoogle....... :)

 

Thanks!

Kimcarrots is offline  
Reply

Tags
Unschooling , Learning Resources , Education , Homeschooling

Quick Reply
Message:
Drag and Drop File Upload
Drag files here to attach!
Upload Progress: 0
Options

Register Now

In order to be able to post messages on the Mothering Forums forums, you must first register.
Please enter your desired user name, your email address and other required details in the form below.
User Name:
If you do not want to register, fill this field only and the name will be used as user name for your post.
Password
Please enter a password for your user account. Note that passwords are case-sensitive.
Password:
Confirm Password:
Email Address
Please enter a valid email address for yourself.
Email Address:

Log-in

Human Verification

In order to verify that you are a human and not a spam bot, please enter the answer into the following box below based on the instructions contained in the graphic.



User Tag List

Thread Tools
Show Printable Version Show Printable Version
Email this Page Email this Page


Forum Jump: 

Posting Rules  
You may post new threads
You may post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are Off