# Multiples and Least Common Multiples (LCM)

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## Objective

SWBAT list the first ten multiples of any whole number less than or equal to 12 and determine the LCM of two whole numbers less than or equal to 12.

#### Big Idea

A multiple is a product of a number and another whole number greater than 0.

7 minutes

To start the lesson, students watch a short clip from Father of the Bride.  The link to the clip can be found here.

After watching the clip, students complete the Think About It problem in pairs.  After 3 minutes of work time, I have students share out their thinking for the hot dog problem.  Some students may have applied the concept of 'multiples', with or without the vocabulary word.  If the word 'multiples' does not come out in discussion, I will bring it up and ask students to help me define it.

## Intro to New Material

10 minutes

After talking about the hot dog problem in the Think About It section, I guide students to fill in the notes on the bottom of the page.

Multiple – a multiple of a number is the product of that number and another whole number greater than 0.

Common multiples – multiples that two of more numbers share.

Least common multiple – the least multiple that two or more numbers share. We can use a Venn diagram or a t-chart to categorize the multiples and common multiples of two numbers.

We then work through the problems in the Intro to New Material section.  The students will first list the multiples of 3 and 4, circling the common multiples.  Then, we'll use a Venn diagram to display the same information.  Either strategy works to find common multiples.  The idea here is to give students multiple options for problem-solving strategies.

## Partner Practice

15 minutes

Students work in pairs on the Partner Practice problem set.  Students may use organized list/charts or a Venn diagram to display their multiples.  I display steps for students as they work, which they can access as a support if they need it:

Steps for Finding the LCM

1)      Write both numbers in a horizontal t-chart.

2)      Next to each number list the first 10 products of that number and the whole numbers starting with 1.

3)      Go number by number in both columns and circle any numbers they have in common.  The first number they have in common is the LCM.

4)       If there is no LCM in the first 10 multiples, keep listing.

As students work, I am circulating around the room and checking in with each group.  I am looking for:

• Are students explaining their thinking to their partner?
• Are students writing their work in the work space, in an organized fashion?
• Are students listing the first 10 multiples of each number when asked?
• Are students correctly identifying the LCM?

• Explain you determined the multiples.
• How did you know these were the common multiples?
• How did you know this was the LCM?
• How does the Venn diagram show the common multiples?
• Is ________ a multiple of ______?  Is ______ a factor of ______? How do you know?

After partner practice time, students complete the Check for Understanding independently.  I then have students clap out the answer.  We talk about each answer choice, using academic vocabulary.

## Independent Practice

20 minutes

Students work on the Independent Practice problem set.

Problem 3 is a great one, that gets students to pause and think.  All of the multiples of 4 will also be multiples of 2.  As students fill in the Venn diagram, they'll be puzzled at first about the right circle being empty.

Problem 7 asks students to apply what they've learned about multiples.  It's a preview of the work that students will do in a future lesson in this unit.

As students work on problems 10 through 12, I am monitoring student work to be sure that students are using academic vocabulary.

## Closing and Exit Ticket

8 minutes

After independent practice time, I have students share out their answers for problems 10-13.  I focus our conversation around using counterexamples to prove that statements are false.  This is an important skill for students to have, and I do expect them to include counterexamples in their strong written responses.

Students independently work on the Exit Ticket to close the lesson.