Question

What is the smallest square number which is divisible by $2,4,5,6$ and $9$?

Answer 1

Step 1: Find the LCM of given numbers.

Apply the prime factorization method to calculate the lcm of the given numbers.

$2=1\times 2$

$4=1\times 2\times 2$

$5=1\times 5$

$6=1\times 2\times 3$

$9=1\times 3\times 3$

So, the required lcm is:

$\begin{array}{rcl}\mathrm{LCM}\left(2,4,5,6,9\right)& =& 2\times 2\times 3\times 3\times 5\\ \therefore \mathrm{LCM}\left(2,4,5,6,9\right)& =& 180\end{array}$

Step 2: Find the least square number we complete the pairs.

$180=2\times 2\times 3\times 3\times 5$

We just needed one $5$ to complete the pair.

We get least square number is:

$2\times 2\times 3\times 3\times 5\times 5=900$

Hence, the required least square number is $900$.