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# What is the LCM of 4, 9, 3?

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sjc Share
Nov 14, 2016

$L C M = 36$

#### Explanation:

List the multiples of each number , then pick the smallest common one.

multiples 4: $\left\{4 , 8 , 12 , 16 , 32 , \textcolor{red}{36} , \ldots . .\right\}$

multiples of 9:$\left\{9 , 18 , 27 , \textcolor{red}{36} , 45 , \ldots . .\right\}$

multiples of 3:$\left\{3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , \textcolor{red}{36} , \ldots\right\}$

$L C M = 36$

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Moksha Share
Sep 23, 2017

The LCM of 4, 9 and 3 is $36$.

#### Explanation:

I'm going to show you 2 methods in which you can get the LCM in this explanation. So let's begin!

Method 1: Write down multiples of 4, 9 and 3.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39

If you don't get a common number soon, then write down more multiples. Or you can quit Method 1 and move onto Method 2.
Speaking of Method 2, now you're going to learn about it!

Method 2: Write down multiples of 9. Just 9. So you're pretty much picking the largest number out of 4, 9 and 3.

9, 18, 27, 36, 45, 54, 63, 72, 81, 90
Now pick a number out of 3 and 4. Then see if that number goes into any multiple. Tip: Start from the first multiple and move on. I picked 4. Does 4 go into 9? Nope.

Does 4 go into 19? Nope.

Does 4 go into 27? Nope.

Does 4 go into 36? Yes!

Now, does 3 go into 36, too? Yes!

You already know that 9 goes into 36 because it is a multiple of 9! So, the LCM will be $36$!

I hope at least one of the methods that I showed you will help you!
My source is my mind, for the methods.

All the best,
Moksha :D

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May 31, 2017

$L C M = 36$

#### Explanation:

First, realise that you do not need to consider the $3$ at all. It is a factor of $9$, so any multiple $9$ is a factor of $3$.

Second: Notice that $4 \mathmr{and} 9$ do not have any common factor, so the LCM has to have all the factors of $4 \mathmr{and} 9$

Look at the product of the prime factors:

$\textcolor{w h i t e}{\ldots \ldots . .} 3 = 3$
$\textcolor{w h i t e}{\ldots \ldots . .} 9 = 3 \times 3$
$\textcolor{w h i t e}{\ldots \ldots . .} 4 = \textcolor{w h i t e}{\ldots \ldots \ldots . .} 2 \times 2$

$L C M = \textcolor{w h i t e}{\ldots} 3 \times 3 \times 2 \times 2 = 36$

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