# Finding the Least Common Multiple (LCM)

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## Objective

SWBAT find the LCM of 2 whole numbers less than or equal to 12

#### Big Idea

The LCM is a useful tool to use when comparing fractions and finding common denominators.

## DO NOW

15 minutes

Pose this question to the students, give them time to start independently, and allow time for partner work after.

Car A leaves town Z at 8 am and travels 60 mph.  Car B leaves town Z 2 hours later and travels at 80 mph in the same direction.  At what time does car B catch up with car A? (answer Car B catches up with Car A at 4pm).

I chose this problem because the students could use a table or a list to solve and in today’s lesson about LCM, we will be using lists.  Additionally, this problem deals with multiples which ties in nicely with LCM.  To encourage student thinking, I would ask them what visual they could represent this problem visually?(SMP 5)  Also, I will have them think about 60 miles per hour and 80 miles per hour? (what do those numbers mean? (SMP 2)  Using these two questions should allow the students to get started on the problem (SMP 1).  Once students have had time to work alone, let them partner up to discuss strategies and solutions (SMP 3).  During this time, I will be walking around making sure students are sticking with the task and trying strategies to come up with an answer.

## Multiples

10 minutes

I will be introducing students to the vocabulary word multiple.  We will go through key words within the definition and I will show them the first example.  I’m going to have the students explain to me why the numbers are multiples of 5? (SMP 2)  Once we have worked through the first example together, I’m going to have the students work on the other examples on their own.  We will then partner up and use mathematical language to explain our answers (SMP 6).

## Using a visual

15 minutes

The students will be looking at a LCM word problem and creating a visual to come up with solution.  I chose this problem because it creates a  visual understanding of what finding the LCM means.  I will giving students time to work out this problem independent.  After a few moments, the students can then partner up to share strategies and solutions.

## Finding the LCM

35 minutes

I will be teaching the students two strategies to find the LCM:  making a list and using the ladder.  The students have used both ways while finding the GCF so they are familiar with how to use each strategy.  The only difference will be how we use the strategies for finding LCM

Since we already looked at finding multiples, I’m going to start with a list first.  The students will be comparing 2 numbers to find their LCM.  Before moving on to a new strategy, I’m going to have the students coming up with the advantages and disadvantages of both the list and the ladder.  Students should work on creating their own list and then we will do a whole group discussion about the pros and cons of both.

Finding the LCM for 4 and 5.  I chose these two numbers because their product is 20 which is the LCM.  I’m going to ask the students, after making the list, if they notice anything about their LCM in relationship to each number.  Also, I’m going to ask them about the GCF of 4 and 5.  I want students to notice that each time you have 2 numbers whose GCF is 1, you will always multiply the numbers together to find the LCM.  This idea will develop over time, not with just one problem. If students are using the ladder, there is always a lot of confusion when they can't find a common factor.  I tell the students that this is a "special case".  When they get to a problem and they can't figure out the common fact, I will ask "what is a factor of every number"? (1).  If one is our common factor then all we have to do is multiply the numbers together.

Finding the LCM for 3 and 9:  I chose these two numbers because 3 is a factor of 9 which makes 9 the LCM.  Again, as we go along, I want the students to be noticing these patterns in math on their own.

Finding the LCM for 6 and 9 & 8 and 12:  I chose this problem because they do have a common factor and it works well in the ladder.  I will be asking the students about the GCF and if 6 is a factor of 9 so they can continue to make sense out of the numbers being used.

When students get to work on their own, I’ve given them numbers that support their learning from each of the examples.  I will be looking to see who uses the “short cut” or who will be using one of the strategies as I walk around to check for understanding.

During this part of the lesson, I want student to look at the word problem and have them tell me how they know they would need to use LCM? (SMP 2).  Are there key words that say LCM?  Is there something happening in the problem that reminds you of finding the LCM?  As students begin thinking about these questions, I’m going to have them write down how they know and then have them solve.  Encourage students that are having difficulty understanding how to get started to draw a picture (SMP 5).

As students finish, do a HUSUPU to get them in groups of two.  Partners can then share their strategies and the results.

## Closure

10 minutes

Students will be completing a self assessment survey for me.  I want to check in with them to see what they feel they know and what they are still struggling with.  I chose 3 questions for them to answer that will help me achieve this.  Have students cut along the dotted line and turn it in.  I will be looking over these to use during stations tomorrow to more effectively help the students.