# Question #8a3cc

Apr 10, 2017

$120$

#### Explanation:

$\textcolor{w h i t e}{\ldots . .} 8$$\textcolor{w h i t e}{123456789}$$12$$\textcolor{w h i t e}{123456789}$$15$
$\ldots \ldots \ldots \ldots \ldots$$\textcolor{w h i t e}{129}$$\ldots \ldots \ldots \ldots$$\textcolor{w h i t e}{1298}$$\ldots \ldots \ldots \ldots .$
$\textcolor{w h i t e}{\ldots . .} 8$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots . .} 12$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} 15$
$\textcolor{w h i t e}{\ldots . .} 16$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} 24$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} 30$
$\textcolor{w h i t e}{\ldots . .} 24$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} 36$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} 45$
$\textcolor{w h i t e}{\ldots . .} 32$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} 48$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} 60$
$\textcolor{w h i t e}{\ldots . .} 40$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} 60$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} 75$
$\textcolor{w h i t e}{\ldots . .} 48$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} 72$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} 90$
$\textcolor{w h i t e}{\ldots . .} 56$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} 84$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} 105$
$\textcolor{w h i t e}{\ldots . .} 64$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} 96$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \textcolor{g r e e n}{120}$
$\textcolor{w h i t e}{\ldots . .} 72$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} 108$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{30}$
$\textcolor{w h i t e}{\ldots . .} 80$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \textcolor{g r e e n}{120}$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{30}$
$\textcolor{w h i t e}{\ldots . .} 88$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{24}$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{30}$
$\textcolor{w h i t e}{\ldots . .} 96$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{24}$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{30}$
$\textcolor{w h i t e}{\ldots . .} 104$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{24}$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{30}$
$\textcolor{w h i t e}{\ldots . .} 112$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{24}$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{30}$
$\textcolor{w h i t e}{\ldots . .} \textcolor{g r e e n}{120}$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{24}$$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \textcolor{w h i t e}{30}$

The LCM is $120$

Apr 10, 2017

$120$

#### Explanation:

The easiest way to do this is to find the prime factorization of each number first.

$8 = 4 \cdot 2$
$8 = 2 \cdot 2 \cdot 2$
$8 = {2}^{3}$

$12 = 6 \cdot 2$
$12 = 3 \cdot 2 \cdot 2$
$12 = 3 \cdot {2}^{2}$

$15 = 5 \cdot 3$

Now that we have reduced all numbers to their prime factorizations, we will look for the factors with the highest exponent and multiply them all together to get our LCM.

There is ${2}^{3}$ from $8$, ${3}^{1}$ from $12$ and $15$, and ${5}^{1}$ from $15$.

So now we must do the following:

${2}^{3} \cdot 3 \cdot 5$
$2 \cdot 2 \cdot 2 \cdot 3 \cdot 5$
$120$

Therefore, the LCM of $8$, $12$, and $15$ is $120$.