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Introduction

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Introduction

Least Common Multiple (LCM)

INTRO
β€”
A multiple of a given number is what you get when you multiply the given number by another number.
Since there is an infinite amount of numbers you can multiply by, there is an infinite amount of multiples for any number. The list goes on and on like magic
.
For example, let’s take a look at multiples of :
Multiples of
The Least Common Multiple (LCM) is the smallest multiple two or more numbers have in common.
Multiples of
Multiples of
When we organize the factors from least to greatest, we can easily see that the LCM of and is .

Least Common Denominator

We can use the LCM to find a common denominator when adding and subtracting fractions. The LCM of the denominators is the least common denominator.
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to find the least common multiple and test your understanding.

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CALCULATOR
β€”

LCM Calculator

Find the least common multiple, or LCM, ofand.

Step 1. Remember what a multiple is.

A multiple is the product of a number with any other number.

Step 2. Find the first multiple of each number.

We start by multiplying each number by .

Step 3. Find the next multiple of each number.

Multiply each number by the next integer.

Step 4. Check for the least common multiple.

Look for a multiple that shows up for both numbers. If you don't see one, repeat Step 3. If you do see one, stop πŸ›‘. This is the least common multiple.
So, the least common multiple, or LCM, is .
KEY STEPS
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How to Find the LCM

Step 1. Remember what a multiple is.

A multiple is the product of a number with any other number.

Step 2. Find the first multiple of each number.

We start by multiplying each number by .

Step 3. Find the next multiple of each number.

Multiply each number by the next integer.

Step 4. Check for the least common multiple.

Look for a multiple that shows up for both numbers. If you don't see one, repeat Step 3. If you do see one, stop πŸ›‘. This is the least common multiple.
LESSON
β€” Finding the LCM

Finding the LCM

A multiple of a given number is what you get when you multiply the given number by another number.
When we have two or more given numbers, we can compare their multiples to see which ones they have in common.
The smallest multiple they share is called the Least Common Multiple (LCM).

What is the difference between GCF and LCM?

Greatest Common Factor (GCF)Least Common Multiple (LCM)
Largest factor two or more numbers have in common.Smallest multiple two or more numbers have in common.
Example: GCF of and is .
Factors of :
Factors of :
Example: LCM of and is .
Multiples of :
Multiples of :

How to find the LCM using the GCF

The LCM of two numbers (let's call them and ) is equal to the product of the two numbers divided by their GCF.For example:
Let’s walk through step-by-step examples of how to find the LCM of numbers!

EXAMPLE 1

Let's start by finding the LCM of and .

Step 1. Remember what a multiple is.

A multiple is the product of a number with any other number.

Step 2. Find the first multiple of each number.

We start by multiplying each number by .

Step 3. Find the next multiple of each number.

Multiply each number by the next integer.

Step 4. Check for the least common multiple.

Look for a multiple that shows up for both numbers. If you don't see one, repeat Step 3. If you do see one, stop πŸ›‘. This is the least common multiple.
So, the least common multiple, or LCM, is .

EXAMPLE 2

Nice work! Now, let's find the GCF of and .

Step 1. Remember what a multiple is.

A multiple is the product of a number with any other number.

Step 2. Find the first multiple of each number.

We start by multiplying each number by .

Step 3. Find the next multiple of each number.

Multiply each number by the next integer.

Step 4. Check for the least common multiple.

Look for a multiple that shows up for both numbers. If you don't see one, repeat Step 3. If you do see one, stop πŸ›‘. This is the least common multiple.
So, the least common multiple, or LCM, is .
Awesome! If you’d like to practice additional problems finding the LCM, expand the
Practice
below before closing out this lesson! ⚑
PRACTICE
β€” Finding the LCM

Practice: Finding the LCM

Question 1 of 10: Find the LCM of 9 and 12.

Step 1. Remember what a multiple is.

A multiple is

Step 2. Find the first multiple of each number.

Start by multiplying each number by .
Multiples of
Multiples of

Step 3. Find the next multiple of each number.

Multiply each number by the next integer.
Multiples of
Multiples of

Step 4. Check for the least common multiple.

Look for a multiple that shows up for both numbers. If you don't see one, repeat Step 3. If you do see one, stop πŸ›‘. This is the least common multiple.
Multiples of
Multiples of
Awesome job! The LCM is Β .

CONCLUSION
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Incredible job, look at you go! Thanks for checking out this lesson β˜ΊοΈπŸ™. Where to next?
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