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Lesson 10: Least common multiple

# Least common multiple of three numbers

The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. To find the LCM, you can list the multiples of each number and find the smallest one they share, or use prime factorization to break down the numbers into their prime factors and multiply the highest powers of each factor. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• can 0 be a multiple?
• one other video i watched that it could. I'm confused
• What is a good tip to memorize this?
• I would say that you need to think whether some of the numbers go into each other, and otherwise just multiply them all together.
• Is the LCM useful in life? Sal should have explained that.
• It is useful.
If u want same amount of things which comes in different groups then it can be useful.

For example you want equal number of pens and pencils.
However the pens come in packets containing 10 pens whereas pencils come in packets containing 16 pencils.

In this case finding the L.c.M you can find out how many packets you have to buy
• So you can find the LCM of 3 numbers the same way as with 2 numbers (such as the Prime Factorization Method)?
• Is it right in thinking that in some cases the LCM is also the HCF/GCF?
• Multiples and Factors are different things. So, the LCM is not also going to be the GCF.

Consider: LCM for the numbers 6 and 8
Multiples of 6 are: 6, 12, 18, 24, 30, 36, etc.
Multiples of 8 are: 8, 16, 24, 32, 40, etc.
The LCM for 6 and 8 = 24 because this is the first multiple they have in common.

Now, let's find the GCF for 6 and 8.
Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8
The GCF for 6 & 8 is 2 because this is the largest common factor for those numbers.

Hope this helps.
• If you have 100000 what would you do?
• Why does Khan Academy point out mistakes? Twice in this video.
• To correct it and so as not to confuse watchers.
• that is the lcm of 5,6 and 7
• 5=5
6=2*3
7=7
So, Lcm=2*3*5*7=210
• Would there be an LCM for a negative number and a positive number?
• Can you explain more please
• the process is really easy! at first, it was difficult for me too. let me summarize this for you,
For LCM :
1. prime factorize the given numbers.
2. pick the highest power of each prime factor.
3 Multiply them! it's that easy!
let me give you an example to understand better,
for example,
52 = 2^2 × 13
78 = 2×3×13
prime factors of both = 2,3,13
highest powers = 2^2, 3, 13
multiply them, you get 2^2×3×13 = 156

and a hack to make it easy to remember,
lowest common multiple needs highest powers,
the highest common factor needs the lowest powers (but only common factors should be selected, not all prime factors like we do for LCM)