Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.12Least Common Multiple

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find the least common multiple (LCM) of two numbers by listing or comparing their multiples.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Least Common MultipleSpanish: Mínimo común múltiplo The least positive number that is a multiple of two or more numbers. Multiples of 4 and 6 first meet at 12, so LCM = 12.
MultipleSpanish: Múltiplo What you get when you multiply a number by 1, 2, 3, and so on. Multiples of 4: 4, 8, 12, 16, 20 — found by multiplying 4 × 1, 4 × 2, 4 × 3, ...
Common multipleSpanish: Múltiplo común A number that two or more numbers both go into. 12, 24, and 36 are all common multiples of both 3 and 4
Skip countingSpanish: Conteo salteado Counting by a number, like 2, 4, 6, to list its multiples. Skip count by 6: 6, 12, 18, 24, 30 — each jump adds 6
Prime factorizationSpanish: Factorización prima Writing a number as prime numbers multiplied together. It helps you find the LCM. 4 = 2 × 2, 6 = 2 × 3. LCM uses the highest power of each prime: 2² × 3 = 12

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

I want the LCM of 4 and 6. I skip count the multiples of 4: 4, 8, 12, 16, 20, 24.

  1. Then I skip count the multiples of 6: 6, 12, 18, 24.
  2. I look for the first number in BOTH lists. 12 is in both lists, and it comes before 24.
  3. So the LCM of 4 and 6 is 12. I check: 12 ÷ 4 = 3 and 12 ÷ 6 = 2, so both go into 12 evenly.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Let's find the LCM of 3 and 5. What are the multiples of 3? (3, 6, 9, 12, 15.)

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The LCM of 4 and 6 is because it is the smallest number in the group.

Word bank Least Common MultipleMultipleCommon multipleSkip countingPrime factorizationleastcommonmultiplesmallest12sharedboth

Watch outA common mistake

A common mistake in Least Common Multiple is multiplying the two numbers together instead of listing multiples to find the smallest shared one. For example, for 4 and 6, a student calculates 4 × 6 = 24 and calls that the LCM, but the actual least common multiple is 12 (multiples of 4: 4, 8, 12; multiples of 6: 6, 12 — 12 is the first number that appears in both lists). This shortcut only works when the two numbers share no common factors (like 4 and 9, where the LCM really is 36 = 4 × 9); for numbers like 4 and 6 that share a factor of 2, multiplying overshoots the true LCM. Always list multiples of both numbers and pick the first one that appears in both lists.

Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.12Least Common Multiple

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the least common multiple (LCM) of two numbers by listing or comparing their multiples.

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    Find the LCM of 5 and 6 on the number line

    036912151821242730

    Hint Read the labels: some marks are multiples of 5 and some are multiples of 6. The LCM is the first spot that belongs to BOTH.

    Show your thinking
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    What is the LCM of 3 and 5?

    1. A3
    2. B5
    3. C15
    4. D30

    Hint LCM is about MULTIPLES (counting UP by each number), not factors. You want the smallest number BOTH lists reach.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    What is the LCM of 6 and 8?

    1. A6
    2. B14
    3. C24
    4. D48

    Hint Careful: 6 + 8 is not a multiple of either number. You need a number that both 6 AND 8 divide into evenly.

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    What is the LCM of 4 and 10?

    1. A2
    2. B10
    3. C20
    4. D40

    Hint The LCM is the smallest number both 4 and 10 count into — it is often much smaller than 4 × 10 = 40.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    What is the LCM of 2 and 7?

    1. A2
    2. B7
    3. C9
    4. D14

    Hint Notice that 2 and 7 are both prime — they share no common factor. That makes this a special, faster case.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot Riley's Mistake — LCM of 4 and 6

    1. 1ProblemFind the LCM of 4 and 6.
    2. 2Multiples of 44, 8, 12, 16
    3. 3Multiples of 66, 12, 18
    4. 4Choose the answerRiley added the two numbers: 4 + 6 = 10, so LCM = 10.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Riley added 4 + 6 to get 10. Check: is 10 in both lists of multiples?

    Correct work
    Correct answer:

Explain your thinkingWhat is the least common multiple of 4 and 6? How did sorting the multiples help you find it?

Sentence starter The LCM of 4 and 6 is ___ because it is the smallest number in the ___ group.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.12Least Common Multiple

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the least common multiple (LCM) of two numbers by listing or comparing their multiples.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each pair of numbers to their LCM.

    1. LCM(2, 5)
    2. LCM(4, 10)
    3. LCM(3, 8)
    4. LCM(6, 9)
    5. LCM(5, 7)
    6. LCM(4, 6)
    • A10
    • B20
    • C24
    • D18
    • E35
    • F12
  2. 2Complete the table. Show how you found each value.

    List multiples of each number until you find the LCM.

    NumbersMultiples of FirstMultiples of SecondLCM
    6 and 10
    8 and 12
    9 and 12
    Show your work
  3. 3Write the name of the correct group on each line.

    Sort each pair: does the LCM equal the product of the two numbers, or is the LCM less than the product?

    Groups: LCM = Product (no shared factors) LCM < Product (shared factors)
    • 3 and 7
    • 5 and 11
    • 2 and 9
    • 4 and 6
    • 6 and 8
    • 10 and 15
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Two buses leave the station at 8:00 AM. Bus A returns every 15 minutes and Bus B returns every 20 minutes. When is the next time both buses are at the station together?

    1. A8:30 AM (30 minutes later)
    2. B8:40 AM (40 minutes later)
    3. C9:00 AM (60 minutes later)
    4. D9:20 AM (80 minutes later)
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot Maya's Mistake — LCM of 6 and 9

    1. 1ProblemFind the LCM of 6 and 9.
    2. 2Multiples of 66, 12, 18, 24
    3. 3Multiples of 99, 18, 27
    4. 4Choose the answerMaya saw that 9 is bigger than 6, so she wrote LCM = 9.

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingWhat is the least common multiple of 4 and 6? How did sorting the multiples help you find it?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 6: Numerical and Algebraic ExpressionsStandard 6.NOS.4

Lesson 6.12Least Common Multiple

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find the least common multiple (LCM) of two numbers by listing or comparing their multiples.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Use prime factorization to find the LCM. Take the highest power of each prime factor.

    NumbersPrime FactorizationsHighest PowersLCM
    12 and 18
    15 and 20
    8 and 14
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find Jaylen's Mistake

    1. 1Find LCM of 8 and 12List multiples of 8 and 12
    2. 2Multiples of 88, 16, 24, 32, 40, 48
    3. 3Multiples of 1212, 24, 36, 48
    4. 4Common multiples24, 48
    5. 5Choose LCMLCM = 48

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    You are making party favors. Glow sticks come in packs of 10 and bracelets come in packs of 4. What is the fewest of each you can buy so every favor has exactly one glow stick and one bracelet with none left over? Explain how the LCM solves this problem.

    Write your answer

Explain your thinkingWhat is the least common multiple of 4 and 6? How did sorting the multiples help you find it?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help