Welcome to Math Class! Today we are learning about: Least Common Multiples

Materials you will need for class: Math journal Math textbook Pencil Eraser Your desk should be cleared except for these four things!

I scream for ice-cream! Sally knows that the ice-cream truck drives by her house every 3 days. On what days can she plan to buy ice- cream from the ice-cream truck?

Solution Example: Multiply a whole number by counting numbers… 3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 The ice-cream truck will come by on days 3, 6, 9, 12, 15, and 18. On what other days will the ice-cream truck come by?

Now you try! Get ready to work with your small group to try some examples. Ready…set…GO!

We all scream for ice-cream! Sally wants to know more information! We already know that the ice-cream truck comes by every 3 days. However, there is another ice-cream truck that drives by Sally’s house every 4 days. When is the next time that both ice-cream trucks will drive by on the same day?

What is our first step? We need to figure out the days that the 1 st ice-cream truck will drive by Sally’s house by identifying multiples of 3. We already did this! How did we solve this part of the problem?

Show our work! 3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30 The first ice-cream truck will come by on days 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30.

What is our second step? We need to figure out what days the 2 nd ice-cream truck will drive by Sally’s house by identifying multiples of 4. How do we do this?

Show our work! 4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40 The second ice-cream truck will come by on days 4, 8, 12, 16, 20, 24, 38, 32, 36, and 40.

What is our next step? We need to figure out the common multiples, or the days when both ice- cream trucks will drive by Sally’s house. How do we do this?

Show our work! Ice-cream truck #1: 3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 15 3 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 30 Ice-cream truck #2: 4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40 Let’s compare the schedule for both ice-cream trucks. On what days will both trucks drive by Sally’s house?

What is our last step? We figured out the days when both ice-cream trucks will drive by Sally’s house, but we’re not done yet! Sally said she wanted to know the next time both trucks will drive by. When will that be? How do we figure this out?

Show our work! We know that both ice-cream trucks will drive by Sally’s house on days 12 and 24. The smallest number is 12. The next time both ice-cream trucks will drive by Sally’s house is on day 12! Great job!

Least Common Multiple We just figured out the least common multiple to solve Sally’s problem! The least common multiple (or LCM) is the smallest factor that two whole numbers have in common.

Example #1 – Let’s work together to find the LCM for the numbers 2 and 5. How should we set up this problem to solve it?

Show our work! 2 x 1 = 2 2 x 2 = 3 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10 2 x 6 = 12 2 x 7 = 14 2 x 8 = 16 2 x 9 = 18 2 x 10 = 20 5 x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25 5 x 6 = 30 5 x 7 = 35 5 x 8 = 40 5 x 9 = 45 5 x 10 = 50 What are the common multiples of 2 and 5? What is the LCM?

Example #2 – Let’s work together to find the LCM for the numbers 10 and 4. How should we set up this problem to solve it?

Show our work! 10 x 1 = x 2 = x 3 = x 4 = x 5 = x 6 = x 7 = x 8 = x 9 = x 10 = x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 40 What are the common multiples of 10 and 4? What is the LCM?

Turn to page 153 in your textbook Let’s take a look at some different ways that we can solve problems involving multiples.

LCM Calculator common-multiple-tool.html Let’s predict what the LCM will be when we use an LCM calculator!

Let’s play a game! Find your math partner and get ready to play Tic-Tac- Toe with least common multiples. One person from each group needs to get a blank game sheet and one deck of cards from the activities bin.

Review What is a multiple? What is one way that we can find multiples of a whole number? What is a least common multiple? How do we figure out the least common multiple for two whole numbers?

HOMEWORKHOMEWORK Complete the LCM worksheet. Remember to show your work for all problems.