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# What is the least common multiple of 9 and 15?

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sjc Share
Feb 28, 2018

$\lcm \left(9 , 15\right) = 45$

#### Explanation:

listing the multiples

multiples of $9 : \text{ } \left\{9 , 18 , 27 , 36 , \textcolor{red}{45} , 54 , 63 , 72 , 81 , \textcolor{red}{90} , 99 , \ldots\right\}$

multiples of $15 : \text{ } \left\{15 , 30 , \textcolor{red}{45} , 60 , 75 , \textcolor{red}{90} , 105 , . .\right\}$

common multiples$\text{ } \left\{45 , 90 , \ldots\right\}$

$\lcm \left(9 , 15\right) = 45$

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#### Explanation

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#### Explanation:

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1s2s2p Share
Feb 26, 2018

$45$

#### Explanation:

First we need to write out the prime factors of $9$ and $15$.

$9 : 3 \times 3$
$15 : 3 \times 5$

Now we group them together:
$9 : \left(3 \times 3\right)$
$15 : \left(3\right) \times \left(5\right)$

Next we take the largest groups of each number:
$9$ has two $3$s while $15$ has 1 $5$.

We multiply the largest groups together:
$L C M \left(9 , 15\right) = 3 \times 3 \times 5 = 45$

$\frac{45}{15} = 3$, $\frac{45}{9} = 5$

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