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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$8 and $10$10

Multiples of 8: 8, comma, 16, comma, 24, comma, 32, comma, start color #11accd, 40, end color #11accd, comma, 48, comma, 56, comma, 64, comma, 72, comma, start color #11accd, 80, end color #11accd, point, point, point
Multiples of 10: 10, comma, 20, comma, 30, comma, start color #11accd, 40, end color #11accd, comma, 50, comma, 60, comma, 70, comma, start color #11accd, 80, end color #11accd, comma, 90, comma, 100, point, point, point
start color #11accd, 40, end color #11accd and start color #11accd, 80, end color #11accd are common multiples of 8 and 10. Which of these is the least?
start color #11accd, 40, end color #11accd is the smallest multiple that 8 and 10 have in common.
start text, l, c, m, end text, left parenthesis, 8, comma, 10, right parenthesis, equals, 40

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

Multiples of 3: 3, comma, 6, comma, 9, comma, start color #11accd, 12, end color #11accd, comma, 15, comma, 18, comma, 21, comma, start color #11accd, 24, end color #11accd, point, point, point
Multiples of 4: 4, comma, 8, comma, start color #11accd, 12, end color #11accd, comma, 16, comma, 20, comma, start color #11accd, 24, end color #11accd, comma, 28, point, point, point
Multiples of 6: 6, comma, start color #11accd, 12, end color #11accd, comma, 18, comma, start color #11accd, 24, end color #11accd, comma, 30, comma, 36, point, point, point
start color #11accd, 12, end color #11accd is the smallest multiple that 3, comma, 4, comma and 6 have in common.
start text, l, c, m, end text, left parenthesis, 3, comma, 4, comma, 6, right parenthesis, equals, 12

## Practice

Problem 1
• Current
What is the least common multiple of 3 and 9?
Another way to say this is:
start text, l, c, m, end text, left parenthesis, 3, comma, 9, right parenthesis, equals, question mark

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.
• This is very easy for me but others who dont get it should watch the video and take down the notes because that is how it helped me. For sure theyre gonna get it next time!
• Tru,or, you can go on mathantics when you don't understand something
• 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!
• how one question make some more question please.
• so this is kinda hard idk how to actually figure it out without looking it up....
• fr it is so hard but if u look it up it make it easier bc u kno the answers and thats wht i like....