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Lesson 10: Least common multiple

# Least common multiple review

Review least common multiples (LCM) and try some practice problems.

## What is LCM?

LCM stands for least common multiple. The least common multiple of two numbers is the smallest number that is a multiple of both of them.

## Finding least common multiple

One way to find the LCM of two (or more!) numbers is to list the multiples of each number until we find the smallest multiple they have in common.

### Example 1: LCM of $8$‍  and $10$‍

Multiples of $8$: $8,16,24,32,40,48,56,64,72,80\text{…}$
Multiples of $10$: $10,20,30,40,50,60,70,80,90,100\text{…}$
$40$ and $80$ are common multiples of $8$ and $10$. Which of these is the least?
$40$ is the smallest multiple that $8$ and $10$ have in common.
$\text{lcm}\left(8,10\right)=40$

### Example 2: LCM of $3,4,$‍  and $6$‍

Multiples of $3$: $3,6,9,12,15,18,21,24\text{…}$
Multiples of $4$: $4,8,12,16,20,24,28\text{…}$
Multiples of $6$: $6,12,18,24,30,36\text{…}$
$12$ is the smallest multiple that $3,4,$ and $6$ have in common.
$\text{lcm}\left(3,4,6\right)=12$

## Practice

Problem 1
What is the least common multiple of $3$ and $9$?
Another way to say this is:
$\text{lcm}\left(3,9\right)=?$

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• I think the easiest way is to write down the multiples and then find it.
• Why do they put the older comments in the top and also there all kind of old.
• I get it i'm just need a little more work that's all.
• When i finished the whole thing for l.c.m i played: i feel good and danced!
• lol thats funny
• how one question make some more question please.
• This is honestly easy
(my opinion)
• so this is kinda hard idk how to actually figure it out without looking it up....
• Did you watch the video? Even if you don't have to it will help out. Just if you watch the video and do the practice, then you will understand a lot more.
(1 vote)
• what is the LCM of 8,10,and 23