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

Lesson 6.126.12 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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.

One light flashes every 6 seconds. Another light flashes every 10 seconds. They flash together now. When will they flash together next? Kai says 6 × 10, or 60 seconds. Is he right?

  1. List the multiples of the larger number, 10: 10, 20, 30, 40
  2. Test each one. Is it a multiple of 6?: 10 no → 20 no → 30 yes
  3. Compare with Kai's answer: 6 × 10 = 60 → 60 ÷ 30 = 2
  4. They flash together again in 30 seconds. Kai is not right. 60 is common, but it is not the least.

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. Then explain why the product works this time.

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 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

  1. 1Complete each step, then write the final answer.
    BusLeaves at (minutes)
    Every 6 min6, 12, ?
    Every 15 min15, ?
    Find the first time in both lists.

    One bus leaves every 6 minutes. Another bus leaves every 15 minutes. They leave together now. In how many minutes will they leave together again?

    1. 1List the multiples of the larger number, 15.
    2. 2Which one is the first multiple of 6?
    3. 3Is 6 × 15 = 90 the answer? Why not?
    Final answer:
  2. 2Complete each step, then write the final answer.
    NumberMultiples
    88, 16, ?
    1414, 28, ?

    Find the LCM of 8 and 14. Then compare it with 8 × 14.

    1. 1List the multiples of 14. Which is the first multiple of 8?
    2. 2Find 8 × 14. How does it compare with the LCM?
    3. 3Why is the LCM less than the product for 8 and 14?
    Final answer:
  3. 3Complete each step, then write the final answer.

    Find the LCM of 12 and 18.

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

    The LCM of 4 and an odd number n is 28. What is n?

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

    Pencils come in boxes of 12. Erasers come in bags of 16. You want the same number of pencils and erasers. What is the fewest pencils you can buy?

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

    Ana says the LCM of two numbers is always their product. Test her rule with 10 and 25. What is the LCM of 10 and 25?

    Show your work
    Final answer:

Explain your thinkingWhen is the LCM of two numbers equal to their product? When is it smaller? Give one example of each.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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