Monthly Archives: June 2011

Least Common Multiple Example

There are two ways to find the LCM given in the textbook (Basic Mathematical Skills with Geometry, 8th Ed. by Baratto and Bergman)

Let’s look at example #4 on page 192 in a little more detail.

One way of doing this problem would be the ‘Listing Method’.  So, to find the LCM of 10 and 18, we could do the following:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, etc…

18, 36, 54, 72, 90, 108, 126, 144, 162, 180, etc…

Note that 90 is the LCM, but 180 is also in common, it’s just not the lowest number in common.  However, we could have already guessed that 180 is in common since 10 times 18 = 180.

Let’s look at the ‘Prime Factorization Method’ now.

10 = 2 x 5  and 18 = 2 x 3 x 3

We have to line up the factors vertically.  This means that a 2 can only be lined up over a 2, a 3 can only be lined up over a 3, a 5 can only be lined up over a 5, etc.

10 = 2           x 5 (The 5 moved over because it can’t be over a 3)

18 = 2 x 3 x 3

Now we count one number from each column.  See the bolded numbers above.  Note that one of the 2’s was repeated (since it was stacked on top of another 2).  If there numbers stacked on top of each number like that, we only count it once.

Thus, we have 2 x 3 x 3 x 5 = 90.

Now, remember the listing method?  Remember how 90 and 180 were both in common?  180 is actually too high simply because it counts the ‘extra 2′ that was stacked when it didn’t need to be counted.

Five Quick Classroom Ideas

I’m not sure if I’ve been absolutely clear on this or not, but my lack of posting lately can be attributed to the fact that I’m now posting a majority of the links I find now on my page (  Nevertheless, here are five quick ideas that just didn’t fit in over there:

1.  Create a Magazine Cover ( — In one of my Pre-Algebra courses last year I had students create a magazine about a chapter in the textbook.  This website would have helped the groups easily make a professional looking magazine cover for their project.

2.  Create Printable Posters ( and ( — In one of my Beginning Algebra courses last year I had students create math ‘movie posters’.  Since I was working at a design school at the time, the students had the luxury of having access to industrial poster printers.  These websites would help in cases where students do not have access to those.

3.  Free Podcast Hosting ( — You would not believe how many times I have said that I want to start podcasting my classes, but I did not have a place to host them.  I think that I will definitely be checking this website out in the near future.

4.  Math Games for Developmental Math ( — Personally, I loved the MATHO game so much the first time I played it on the web that I was willing to pay $0.99 for the APP to entertain myself on my Android Phone.  But that may be because I’m really just not an Angry Birds kind of guy.

5.  Math in Everyday Life Videos ( — Yes, I know, the last thing we all need is a link to more math videos.  The only reason that I thought that this site stood out is because of the organization of the categories, including a category for ‘Math in Everyday Life’.

CPR: Compression-only, Hands-only CPR

Please let this video serve as a reminder that although we hope we never have to use CPR in the classroom, in the case that we do, we should be prepared. Please take 60 seconds of your time to watch this very important message. Thanks.
And by the way, every medical emergency I have ever had in the classroom has occured while teaching during the summer semester.