As a K–12 academic content writer and education strategist with over a decade of experience, I’ve seen how mastering basic number concepts early on can set students up for long-term math success. One such foundational concept is the common multiple.
Understanding common multiples plays a vital role in learning about fractions, least common multiples (LCM), and solving real-life math problems like scheduling or dividing items evenly. In this article, we’ll break down exactly what a common multiple is, why it matters, and how to find it easily—with examples and tips tailored for students, parents, and teachers alike.
Let’s make math make sense—one multiple at a time.
What Is a Common Multiple?
What Is a Multiple in Math?
Before we can define a common multiple, we need to understand what a multiple is.
A multiple of a number is what you get when you multiply that number by whole numbers.
For example:
- Multiples of 3 are: 3, 6, 9, 12, 15, 18, …
- Multiples of 5 are: 5, 10, 15, 20, 25, …
These lists go on forever because you can always multiply by a bigger number.
What Is a Common Multiple?
A common multiple is a number that is a multiple of two or more numbers.
Example:
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, …
- Multiples of 6: 6, 12, 18, 24, 30, …
- Common multiples of 4 and 6: 12, 24, 36, …
So, 12 and 24 are common multiples of both 4 and 6.
What Is the Least Common Multiple (LCM)?
The least common multiple is simply the smallest number that is a common multiple of two (or more) numbers.
From the above example:
- LCM of 4 and 6 = 12
Learning the LCM is especially important when adding or subtracting fractions with different denominators.
How to Find Common Multiples
There are several ways to find common multiples. Some methods work best for younger students, while others are ideal for more complex problems.
1. Listing Multiples
This is the simplest method—great for 4th and 5th graders.
Steps:
- Write out the first several multiples of each number
- Look for numbers that appear in both lists
Example:
Find common multiples of 3 and 4
- Multiples of 3: 3, 6, 9, 12, 15, 18
- Multiples of 4: 4, 8, 12, 16, 20
- Common multiple = 12
2. Prime Factorization Method (for LCM)
This method is better for higher grades (5th and up) or when numbers are larger.
Steps:
- Break each number into its prime factors
- Multiply the highest power of all primes
Example:
Find LCM of 8 and 12
- 8 = 2 × 2 × 2
- 12 = 2 × 2 × 3
- LCM = 2 × 2 × 2 × 3 = 24
So, 24 is a common multiple of both.
3. Multiples Table Method
For visual learners, a multiples table or chart is helpful. This is especially effective in classrooms.
You can:
- Create a grid showing the first 10 multiples of each number
- Highlight overlapping values
Many platforms like WuKong Math use colorful tables and games to reinforce this concept with engaging visuals.
4. Digital Tools & Practice Resources
Online learning tools make practice more engaging.
- WuKong Math, for example, provides curriculum-aligned lessons on multiples, LCM, and factors.
- Students can solve interactive problems that reinforce these ideas using gamified formats.
Why Learning Common Multiples Matters
Real-Life Math Applications
Students use common multiples in real-world scenarios all the time, often without realizing it.
Examples:
- Scheduling classes or events (e.g., something repeats every 4 days and another every 6—when do they overlap?)
- Dividing items evenly (e.g., 12 slices of pizza shared equally)
For Test Prep and Problem-Solving
In standardized math tests (e.g., state assessments, NWEA MAP, IXL, or even Kumon), questions involving LCM and multiples appear frequently between Grades 4 and 6.
Mastering these skills early:
- Improves computation fluency
- Builds confidence with fractions, ratios, and word problems
Common Core and Curriculum Alignment
In U.S. Common Core and international curriculums (Singapore Math, Cambridge, etc.), the concept of multiples appears in:
- Grade 4: Understand factors and multiples
- Grade 5: Use LCM for fraction addition/subtraction
- Grade 6–7: Problem-solving with GCF and LCM
Programs like WuKong Math are aligned with these standards, offering structured lessons tailored by grade level.
Examples of Common Multiples in Action
Basic Example: Multiples of 2 and 5
- Multiples of 2: 2, 4, 6, 8, 10, 12…
- Multiples of 5: 5, 10, 15, 20…
Common multiples: 10, 20, 30…
LCM = 10
Intermediate Example: Multiples of 6 and 8
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42
- Multiples of 8: 8, 16, 24, 32, 40
Common multiple = 24
LCM of 6 and 8 = 24
Real-Life Example: Class Schedules
Suppose:
- Science class is every 3 days
- Art class is every 4 days
Question: When will they happen on the same day? - Multiples of 3: 3, 6, 9, 12…
- Multiples of 4: 4, 8, 12…
Answer: Day 12
This is the LCM of 3 and 4
Tips for Teaching or Learning Common Multiples
For Parents
- Use everyday examples:
- Cut pizza slices into equal parts
- Count steps or car wheels
- Encourage games with patterns:
- “Clap every 3 beats, stomp every 5. When do both happen together?”
- Consider supplemental platforms like WuKong Math for guided practice with feedback.
For Teachers
- Use number charts or color-coded multiples on whiteboards
- Incorporate peer teaching (students explain answers to each other)
- Assign fun worksheets with “find the LCM” puzzles
For Students
- Use multiplication charts to see overlaps
- Practice skip counting aloud
- Use digital flashcards or apps with LCM games
Remember: The more you see multiples in patterns, the easier they become to spot!
Final Thoughts
Understanding common multiples is a critical part of elementary and middle school math. Whether you’re adding fractions, solving puzzles, or figuring out when two events overlap, common multiples—and especially the least common multiple (LCM)—show up everywhere.
By using methods like listing, prime factorization, and visual tables, students can grasp the concept with clarity. Parents and teachers can help by relating math to everyday life and practicing with engaging tools.
If your child needs extra support, structured programs like WuKong Education offer personalized guidance from expert teachers—making it easier to master key topics like common multiples and beyond.
I have been deeply involved in the K12 education field for many years and have rich professional knowledge.