Talk:Least common multiple/Student Level

Article Checklist for "Least common multiple/Student Level"

Workgroup category or categories	Mathematics Workgroup [Categories OK]
Article status	Developed article: complete or nearly so
Underlinked article?	Yes
Basic cleanup done?	Yes
Checklist last edited by	David Martin 18:13, 14 May 2007 (CDT)

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Excellent article in progress! Anyone have any comments to make? I wouldn't be surprised if this goes up for approval quickly. - Greg Martin 23:54, 13 May 2007 (CDT)

Thank you.

I think more should be added before approval. Maybe some stuff about polynomials, some more applications, some things about somewhat abstract number theory... Michael Hardy 13:43, 14 May 2007 (CDT)

I'd be happy to write up a section on finding the least common multiple of polynomials. I'm actually teaching this section right now so it's fresh in my mind. I'll get on it today David Martin 13:17, 15 May 2007 (CDT)

Cancelling before multiplying

Nice, easy-to-read article.

Where it says "Note: Always cancel before multiplying." I would suggest something gentler such as "Note: The arithmetic is simpler if you cancel before multiplying," since if you multiply first and then cancel you will still get the right answer. --Catherine Woodgold 20:35, 14 May 2007 (CDT)

I think the comment should be made stronger. Citing only simplicity of arithmetic understates the point. It is frustrating to keep finding students who are alleged to have passed high-school algebra neglecting this point and acting just as if they've never heard of it. (OK, I'm going to restrain myself from getting carried away about engineering students who can't do arithemetic correctly with or without a calculator.) I'd attend to it instantly but for one fact: The most cogent way of illustrating this point is probably by citing some examples of horrible things that can happen when it is neglected. But it may be cumbersome to think of a simple example that does not get far too far from the present topic. Possibly this should be expanded on in some article on algebra when a link and a stern reminder here. Michael Hardy 16:42, 19 May 2007 (CDT)

OK, maybe the part about doing arithmetic should become a separate article. Students seem FAR too ready to believe uncritically everything they get from a correctly functioning calculator. Often they use calculators as anesthetics rather than for calculation... Michael Hardy 16:45, 19 May 2007 (CDT)

I look forward to eventually finding out what the other reason(s) is/are. --Catherine Woodgold 17:45, 19 May 2007 (CDT)

A suggestion

As a high school math teacher, I have to teach this concept all the time. My first suggestion would be to use smaller numbers in the example for the prime factorization method. It's hard to comprehend with such large numbers and so many prime factors. Maybe use 4 and 18. Then, offer a second example using larger numbers. This makes it much more accessible to the common reader.

Also, format the prime factors like so:

${04}={2}\times {2}$

${18}={2}\times$______${3}\times {3}$

     $={2}\times {2}\times {3}\times {3}={36}$

Then you just have to bring down one of each factor per column.

If you were to add a third number to the mix, it'd look like:

${04}={2}\times {2}$

${10}={2}\times$______________$\times {5}$

${18}={2}\times$______${3}\times {3}$

     $={2}\times {2}\times {3}\times {3}\times {5}={180}$

Is this too teacherish for the an article entry? David Martin 13:15, 15 May 2007 (CDT)

I'm going to think about this and some suggestions by Larry Sanger, and probably add some stuff on polynomials. Michael Hardy 22:52, 15 May 2007 (CDT)

As for the question, "Is this too teacherish?" I think that at this level we should be targeting the potential audience which will probably not be graduate students but very young students who are learning this for the first time. Giving numerous simple examples is an advantage here. In addition, this approach will make the entire CZ more accessible for a broader range of readers, in this case teachers as well as students. The ability to explain things simply and provide examples will be well and truly appreciated. --Thomas Simmons 18:37, 19 May 2007 (CDT) +11 hours (EPT)

Article intro

In reading the article intro, I have two points. The first is that it states that the LCM of 9 and 12 is 36 without any explantion. To the common reader, this is not intuitive. It might help to actually list the multiples to show that 36 is the first common multiple (and thus the least).

Also, the application in finding the LCD to add/suntract fractions seems misplaced. It might fit better in a section on applications of the concept. I just feel like a reader will not get the application until after reading the sections on finding it. ...said user:David Martin (talk) (Please sign your talk page posts by simply adding four tildes, ~~~~.)

I think it's OK as it is on this point. Some readers will simply accept the statement that it is the smallest multiple; others will do the rather simple arithmetic to check this for themselves. Just convincing oneself that there don't seem to be any smaller common multiples (or that there certainly aren't) can be done quickly in one's head by many people, I think. --Catherine Woodgold 17:50, 19 May 2007 (CDT)