Math › 6th Grade › Least Common Multiple (LCM)

6th Grade · Math

Least Common Multiple (LCM)

Free sample questions, a clear explanation, and 5 practice skills with an AI tutor that guides without giving the answer away.

Concept Review

Least Common Multiple: When Patterns Meet

Imagine you have two friends with very different schedules. Sarah visits the library every 4 days, and Marcus visits every 6 days. If they both went today, when will they bump into each other again? The answer lies in finding their Least Common Multiple (LCM).

The Least Common Multiple is the smallest number that appears in the multiplication patterns of two or more numbers. Think of it as finding when different rhythms sync up perfectly.

Building the Pattern: List the Multiples

To find the LCM, we list out the multiples of each number like counting by that number:

Sarah's schedule (multiples of 4):

4, 8, 12, 16, 20, 24, 28, 32, 36...

Marcus's schedule (multiples of 6):

6, 12, 18, 24, 30, 36, 42...

They'll meet again on day 12 — that's the LCM of 4 and 6!

The Hunt for Common Ground

When we list multiples, we're looking for numbers that appear in both lists. These are called common multiples. The smallest one is our LCM. It's like finding the first time two different drum beats line up perfectly.

🔍 Surprising Discovery

Sometimes the LCM is one of the original numbers! For example, the LCM of 3 and 9 is just 9, because 9 already contains 3's pattern. But other times, like with 8 and 12, the LCM is 24 — a completely new number that both patterns share.

LCM in Action: More Examples

LCM of 2 and 5

2: 2, 4, 6, 8, 10...

5: 5, 10...

LCM = 10

LCM of 3 and 8

3: 3, 6, 9, 12, 15, 18, 21, 24...

8: 8, 16, 24...

LCM = 24

🔑 Key Takeaway

Just like Sarah and Marcus needed to find when their different schedules would align, the LCM helps us find when different number patterns sync up. It's the mathematical way to predict when separate rhythms will meet again — whether it's library visits, bus schedules, or any repeating pattern in our world.

Sample questions

1. What is the LCM of 4 and 6?

○ 12

○ 24

○ 2

✓ 12? Multiples of 4: 4,8,12,16...; of 6: 6,12,18...; first common is 12

○ 12

Answer: 12? Multiples of 4: 4,8,12,16...; of 6: 6,12,18...; first common is 12 — The least common multiple is 12.

2. Find the LCM of 3 and 5.

○ 15

○ 8

○ 10

✓ 15? Multiples of 3: 3,6,9,12,15...; of 5: 5,10,15...; LCM = 15

○ 15

Answer: 15? Multiples of 3: 3,6,9,12,15...; of 5: 5,10,15...; LCM = 15 — LCM = 15.

3. What is the LCM of 6 and 8?

○ 24

○ 48

○ 2

✓ 24? Multiples of 6: 6,12,18,24...; of 8: 8,16,24...; LCM = 24

○ 24

Answer: 24? Multiples of 6: 6,12,18,24...; of 8: 8,16,24...; LCM = 24 — LCM = 24.

Skills in this topic

List multiples to find the least common multiple of two whole numbers less than or equal to 12
Use prime factorization to find the LCM
Understand the relationship between GCF and LCM
Solve real-world problems involving repeating events or schedules using LCM
Use the LCM to add and subtract fractions with unlike denominators

Practice 50+ questions on this topic

Unlimited interactive practice, progress tracking, and Nova — your AI tutor. Free to start.

Start learning free →