Question

Find the smallest square number that is divisible by each of the numbers $4,9$ and $10$.

• A. $900$
• B. $800$
• C. $1000$
• D. $1200$

Answer 1

The correct option is A $900$

The smallest number divisible by each one of the numbers $4,9$ and $10$ is their LCM, which is $(2\times 2\times 9\times 5)$, i.e., $180$.
Now, $180=\underset{–}{2\times 2}\times \underset{–}{3\times 3}\times 5$
To make it a perfect square, it is multiplied by $5$.
$\underset{–}{2\mid 4-9-10}\mid 2-9-5$
$\therefore$ Required number $=180\times 5=900$