Grade 6 Math · Topic 35

Least Common Multiple (LCM)

The least common multiple (LCM) of two numbers is the smallest positive number that both divide into evenly. The LCM is the go-to tool for adding and subtracting fractions, and for any problem about events that repeat on different cycles.

Lesson alignment: 6.NS.B.4 · Take your time. You can return to this lesson whenever you need it.

Explore visually

Find the first shared multiple

List multiples of both numbers until the same value appears in each list.

Think first: Which multiple do you predict will be the first one in both lists?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

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Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Find the LCM of 8 and 12.

Start by writing the calculation clearly: 8 = 2³, 12 = 2² × 3. Take each prime at the larger exponent: 2³ and 3¹. LCM = 8 × 3 = 24.

Answer: 24

Worked example 2

Find the LCM of 15 and 20.

Start by writing the calculation clearly: 15 = 3 × 5, 20 = 2² × 5. LCM = 2² × 3 × 5 = 60.

Answer: 60

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. lcm(3, 4) =
    Check

    12

  2. lcm(5, 6) =
    Check

    30

  3. lcm(8, 10) =
    Check

    40

  4. lcm(9, 12) =
    Check

    36

  5. lcm(6, 8) =
    Check

    24

  6. lcm(10, 15) =
    Check

    30

  7. lcm(12, 18) =
    Check

    36

  8. lcm(14, 21) =
    Check

    42

Try this situation 1

Bus A leaves every 12 minutes. Bus B leaves every 18 minutes. They just left together. In how many minutes will they leave together again?

Show a worked solution

Answer: 36 minutes.

Start by writing the calculation clearly: lcm(12, 18) = 36.

Try this situation 2

Hot dogs come in packs of 10; buns come in packs of 8. What is the smallest number you can buy of each to have equal counts?

Show a worked solution

Answer: 40 of each (4 packs of hot dogs, 5 packs of buns).

Start by writing the calculation clearly: lcm(10, 8) = 40.

Fresh questions · saved on this device

Practice this skill

34 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

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Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. What is the least common multiple (LCM) of 4 and 6?

2. Two buses stop at the same station. Bus X comes every 9 days and Bus Y comes every 12 days. If both stop today, in how many days will they both stop again on the same day?

3. What is the least common multiple (LCM) of 12 and 18?

4. Two timers beep at regular intervals. Timer A beeps every 24 seconds, and Timer B beeps every 32 seconds. If both beep together now, after how many seconds will they beep together again?

5. A store sells muffins in packages of 4 and doughnuts in packages of 6. What is the least number of packages needed to have the same total number of each?

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

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More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Factors, Multiples & Percents quiz ↗Try a full practice test ↗