R4 · Lesson 4: Least Common Multiple (LCM)

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Why this matters for Grade 6: 6.NS.4 uses the LCM to add and subtract fractions with unlike denominators — you need the LCM of the denominators to find a common denominator. Knowing LCM now means fractions in Grade 6 will be much smoother.

Learn It

Finding the LCM by Listing Multiples

A multiple of a number is the result of multiplying it by 1, 2, 3, 4, … The Least Common Multiple (LCM) of two numbers is the smallest number that appears in both lists of multiples.

Example 1 — LCM(4, 6):

Multiples of 4: 4, 8, 12, 16, 20, 24, …

Multiples of 6: 6, 12, 18, 24, …

The first number on both lists is 12.

LCM(4, 6) = 12

Example 2 — LCM(3, 5):

Multiples of 3: 3, 6, 9, 12, 15, 18, …

Multiples of 5: 5, 10, 15, 20, …

First common multiple: 15.

LCM(3, 5) = 15

Word problem connection: LCM answers "after how many steps do two repeating events first happen at the same time?"

Example 3 — Word problem:
Bus A comes every 4 minutes. Bus B comes every 6 minutes. They both arrive at minute 0. After how many minutes will they next arrive together?

Answer: LCM(4, 6) = 12 minutes. Both buses arrive together again at minute 12.

Try It · Guided

Work These Together

1. What is LCM(4, 6)?

Hint

Multiples of 4: 4, 8, 12, … Multiples of 6: 6, 12, … The first match is 12.

2. What is LCM(3, 5)?

Hint

Multiples of 3: 3, 6, 9, 12, 15, … Multiples of 5: 5, 10, 15, … First match is 15.

Practice · On Your Own

You Try

3. What is LCM(6, 8)?

Hint

Multiples of 6: 6, 12, 18, 24, … Multiples of 8: 8, 16, 24, … First match is 24.

4. A red light blinks every 3 seconds. A blue light blinks every 4 seconds. They both blink at second 0. After how many seconds will they both blink at the same time again?

Hint

Find LCM(3, 4). Multiples of 3: 3, 6, 9, 12, … Multiples of 4: 4, 8, 12, … First common multiple is 12.

5. Which is the correct LCM(2, 7)?

Hint

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, … Multiples of 7: 7, 14, … First match is 14. (Since 2 and 7 share no common factors other than 1, LCM = 2 × 7 = 14.)

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Exit Ticket

Show What You Know

6. What is LCM(5, 10)?

Hint

Multiples of 5: 5, 10, … Multiples of 10: 10, … The first match is 10. (When one number is a multiple of the other, the LCM is the larger number.)

7. Jana does push-ups every 6 days and sit-ups every 9 days. She does both today (day 0). After how many days will she first do both exercises on the same day again?

Hint

Find LCM(6, 9). Multiples of 6: 6, 12, 18, 24, … Multiples of 9: 9, 18, 27, … First common multiple is 18. So the answer is 18 days.

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