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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Find the LCM of 3 and 5. Then explain why the product works this time. List the multiples of 5. Which is the first multiple of 3? (5, 10, 15 → 15) What is 3 × 5? Is it the same as the LCM? (3 × 5 = 15. Yes, it is the same.) Why is the LCM the product here, but not for 6 and 10? (3 and 5 share no factor except 1. 6 and 10 share the factor 2, so their LCM is smaller.)

   Show your work
2. 2

   Warm restartA board 6 feet long is cut into pieces 3/4 foot long. How many pieces are there?

   1. A2 pieces
   2. B4 1/2 pieces
   3. C8 pieces
   4. D24 pieces

   How do you know?
3. 3

   Warm restartA recipe needs 2/3 cup of oats per serving. How many servings can be made from 4 cups?

   1. A1 1/2 servings
   2. B2 2/3 servings
   3. C6 servings
   4. D8 servings

   How do you know?
4. 4

   Warm restartA runner covers 2 1/2 miles in 1/2 hour. What is the speed in miles per hour?

   1. A1 1/4 miles per hour
   2. B2 miles per hour
   3. C3 miles per hour
   4. D5 miles per hour

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhat is the LCM of 8 and 6?

   1. A12
   2. B14
   3. C24
   4. D48

   Why is that the answer?
2. 6

   Think it throughHow many packs of hot dogs do you buy?

   1. A2
   2. B3
   3. C4
   4. D6

   How do you know? Give a second reason as well.
3. 7

   Think it throughHow many packs of buns do you buy?

   1. A3
   2. B4
   3. C5
   4. D6

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelWhat is the least common multiple of 4 and 6? How did sorting the multiples help you find it?

Use the words

Fill each blank with a word from the bank.

• The smallest number that is a multiple of both is their ___ ___ ___.
• The product of a number and any whole number is a ___ of that number.
• A multiple that two or more numbers share is a ___ multiple.
• Counting forward by a number other than 1, like 6, 12, 18, is called ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Least Common Multiple is multiplying the two numbers together instead of listing multiples to find the smallest shared one.
2. 10

   Say moreYou skip counted the multiples of 4 and 6. How did you find the least common multiple from your lists?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Two robotic arms on Station Helios run on repeating cycles. Arm A resets every 9 minutes and Arm B resets every 15 minutes. Right now both arms just reset at the same moment.

   Show your work

Last check

These two come from Lesson 6.11. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — What is the LCM of 9 and 12?

   1. A3
   2. B36
   3. C72
   4. D108

   Explain your choice.
2. 13

   From Lesson 6.11Explain your thinking — A pipe is 3/4 meter long. Each connector piece is 3/8 meter. How many connectors fit on the pipe?

   1. A2
   2. B3/2
   3. C6
   4. D9/32

   How do you know?
3. 14

   From Lesson 6.11Is 10 tests a reasonable answer?

   1. ANo — the answer should be less than 1
   2. BYes — each test uses far less than the total, so the answer should be well above 1
   3. CNo — you cannot divide fractions
   4. DYes — because 10 is a round number

   How do you know?

Be honest — this tells your teacher what to do next