# What is the LCM of 15, 6, and 9?

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14
Sep 3, 2017

$L C M = 90$

#### Explanation:

Write each number as the product if its prime factors:

$\textcolor{w h i t e}{\times x} 6 = 2 \times 3$
$\textcolor{w h i t e}{\times x} 9 = \textcolor{w h i t e}{\times x} 3 \times 3$
$\textcolor{w h i t e}{\times x} 15 = \textcolor{w h i t e}{\times} 3 \textcolor{w h i t e}{\times x} \times 5$

$L C M = 2 \times 3 \times 3 \times 5 = 90$

OR, using the powers:

$6 = \textcolor{b l u e}{2} \times 3$
$9 = \textcolor{b l u e}{{3}^{2}}$
$15 = 3 \times \textcolor{b l u e}{5}$

To find the LCM, use the highest power of each base

$L C M = \textcolor{b l u e}{2 \times {3}^{2} \times 5} = 90$

Or just look at the multiples of $15$ (the biggest number) until you find one which is even (because of 6) and divisible by $9$ (Sum of the digits must be $9$)

$15 , 30 , 45 , 60 , 75 , \textcolor{b l u e}{90}$

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