Question

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

Answer 1

To find smallest square number that is divisible by each of the numbers $4,9$ and $10$, first we need to find LCM of $4,9$ and $10$.

$4=2\times 2=2^2$

$9=3\times 3=3^2$

$10=2\times 5$

LCM $=$ Product of the highest power of common prime factors and other prime factors.

$\Rightarrow$ LCM $=2^2\times 3^2\times 5$

$\Rightarrow$ LCM $=4\times 9\times 5$

$\Rightarrow$ LCM $=180$

Now, lets move to multiples of $180$.

$180\times 2=360$ is not a perfect square.

$180\times 3=540$ is not a perfect square.

$180\times 4=720$ is not a perfect square.

$180\times 5=900$ is a perfect square.[ Since, ${30}^2=900$]

Hence, the smallest square number that is divisible by each of the numbers $4,9$ and $10$ is $900$.