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

Lesson 6.126.12 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find the least common multiple (LCM) of two numbers by listing or comparing their multiples — one step at a time, with support.

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.

Find the least common multiple (LCM) of 4 and 6.

  1. List the multiples of 4: 4, 8, 12, 16, 20, 24
  2. List the multiples of 6: 6, 12, 18, 24
  3. Find the first number in both lists: 12
  4. Check that 4 and 6 both divide 12: 12 ÷ 4 = 3 → 12 ÷ 6 = 2
  5. The LCM of 4 and 6 is 12.

Now you trySame steps, your turn

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

Find the LCM of 3 and 5.

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 6.126.12 Small Group · Group 1

Group 1Supported practice

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

Learning target With my small group, I can find the least common multiple (LCM) of two numbers by listing or comparing their multiples — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    NumberMultiples
    44, 8, ?
    1010, ?
    Skip count until a number is in both lists.

    Find the least common multiple (LCM) of 4 and 10.

    1. 1Skip count by 4. What are the multiples of 4?
    2. 2Skip count by 10. What are the multiples of 10?
    3. 3What is the first number in both lists?
    Final answer:
  2. 2Complete each step, then write the final answer.
    NumberMultiples
    44, ?
    88, ?
    Start with the larger number.

    Find the LCM of 4 and 8.

    1. 1Skip count by the larger number, 8.
    2. 2Is 8 a multiple of 4? How do you know?
    3. 3What is the LCM of 4 and 8?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the LCM of 2 and 7.

    Show your work

    Hint Skip count by 7. Find the first one that is also a multiple of 2.

    Final answer:
  4. 4Complete each step, then write the final answer.

    Find the LCM of 6 and 8.

    Show your work

    Hint Skip count by 8. Test each multiple. Is it also a multiple of 6?

    Final answer:
  5. 5Complete each step, then write the final answer.

    Hot dogs come in packs of 10. Buns come in packs of 8. You want the same number of hot dogs and buns. What is the fewest hot dogs you can buy?

    Show your work

    Hint The number must be a multiple of 10 and a multiple of 8. Find the least one.

    Final answer:
  6. 6Complete each step, then write the final answer.

    Jay says the LCM of 6 and 9 is 54 because 6 × 9 = 54. Is he right? What is the LCM?

    Show your work

    Hint Make the lists. Is there a common multiple less than 54?

    Final answer:

Explain your thinkingJay used 6 × 9 to find the LCM. Why is the product not always the LCM? Use the lists to explain.

Sentence starter The LCM is ___ because it is the first number in ___. · The product ___ is a common multiple, but ___.

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