Question

Find the smallest square which is divisible by $8,12$ and $15$.

• A. $3600$
• B. $4900$
• C. $6400$
• D. $2500$

Answer 1

The correct option is A $3600$

First we will find the LCM of $8,12$ and $15$.
The LCM of $8,12$ is $\underset{–}{2\times 2}\times 2\times 3\times 5=120$.
The prime factors of $120$ are
$120=\underset{–}{2\times 2}\times 2\times 3\times 5$
We can see that $2,3$ and $5$ do not have a pair.

So, we need to multiply $120$ by $2\times 3\times 5=30$
$120\times 30=3600\Rightarrow \sqrt{3600}=60$
$3600$ is a perfect square and it is divisible by $8,12$ and $15$.

$\frac{3600}{8}=450,\frac{3600}{12}=300,\frac{3600}{15}=240$
The smallest perfect square divisible by $8,12$ and $15$ is $3600$.