You Can See the Least Common Multiple: Hands-On Math in ElementaryHow Montessori Children Discover LCM with Their Own Hands

How do you explain the least common multiple to an 8-year-old?

How do you explain the least common multiple to an 8-year-old?

In traditional teaching, we often start with an abstract definition: "The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the numbers considered."

Clear, right?

For an adult, perhaps yes. For a child who is building their mathematical thinking, this sentence is just a sequence of meaningless words.

In the Montessori approach, instead, children see the multiples meeting.

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What Happened in Class This Week

The elementary children worked with the Montessori multiple board: a wooden board with regular holes arranged in rows and columns, where they insert small colored pegs.

The work seems simple, but it's deeply mathematical:

Step 1: Children choose two numbers to explore (for example, 3 and 4)

Step 2: They take pegs of one color and insert them following the pattern of multiples of 3: one at position 3, one at 6, one at 9, one at 12, and so on

Step 3: With pegs of another color, they do the same with multiples of 4: position 4, 8, 12, 16...

Step 4: They observe. They search. They reason.

"Where do the two patterns meet for the first time?"

When they saw that at position 12 there were pegs of both colors - the first meeting point - they discovered the least common multiple.

They didn't learn it. They understood it.

And when they understood the mechanism? They didn't stop. They challenged themselves, taking the work to a higher level: they started searching for the least common multiple of 3, 4, 5, and 6 simultaneously. Hours of deep, voluntary, joyful concentration.

This is what happens when mathematics is not an imposition, but a discovery.

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Why This Approach Works

Maria Montessori understood something fundamental about the mind of the child between 6 and 11 years: it's ready for abstraction, but still deeply connected to concrete experience.

"What the hand does, the mind remembers."

Offering material that makes a mathematical concept visible allows the child to:

✓ Manipulate the idea before naming it - hands explore before the mind defines

✓ See patterns emerge from their own actions - it's not the teacher explaining, it's the material revealing

✓ Build deep understanding, not just mechanical memory - that knowledge truly becomes theirs

✓ Self-regulate the challenge - the child decides when they're ready to increase complexity

As Confucius said centuries ago: "Tell me and I will forget, show me and I will remember, involve me and I will understand."

The child who has experienced the least common multiple with their own hands will never forget it. And when, later on, they encounter the abstract definition, they'll already have a solid mental image to anchor it to.

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How to Explore Multiples at Home

Don't have the Montessori multiple board? No problem! The essence of the approach isn't in expensive material, but in making the invisible visible.

Here are 3 simple ways to explore multiples with your child:

1. With Lego or building blocks

Build two towers together following different rules:

• Red tower: add one block every 3 "turns"

• Blue tower: add one block every 4 "turns"

After how many turns are the towers the same height for the first time? That's the LCM!

Advanced challenge (just like our children did): add a third and fourth tower with different patterns. When are all four the same height?

2. In the kitchen (children's favorite!)

On a long table, place:

• Red cups every 3 positions (3, 6, 9, 12...)

• Blue plates every 4 positions (4, 8, 12, 16...)

Where do they overlap? That's the least common multiple! Bonus: fill them with snacks and celebrate the mathematical discovery

3. Walking (math in motion)

Create a path with 20-30 squares (chalk on the floor or post-its in the hallway).

• First round: jump every 2 squares and place a marker

• Second round: jump every 3 squares and place a different marker

On which numbers do you find both markers? You're seeing common multiples!

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The Value of the Concrete Approach

The Montessori approach to mathematics isn't "easier" - it's more true.

It allows children to build solid foundations on which to then develop abstract thinking. A child who has discovered patterns of multiples with their own hands will be a teenager who navigates fractions, equations, and geometry with confidence and intuition.

Because that mathematics isn't something someone told them. It's something they lived.

And when a child gets so excited that they work for hours on a mathematical concept, self-increasing the difficulty without anyone asking them to, we know we've done something right.

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Want to Learn More About the Montessori Method for Elementary?

Every week we share:

• What children are discovering in class

• How Montessori materials work

• Hands-on activities to do at home

• The pedagogical "why" behind every approach

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P.S. - Have questions about the Montessori method for ages 6-11? Write to us! We're here to support families on their educational journey.

P.S. - Have questions about the Montessori method for ages 6-11? Write to us! We're here to support families on their educational journey.