# Ex.6.3 Q9 Squares and Square Roots Solutions - NCERT Maths Class 8

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## Question

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

## Text Solution

What is known?

Divisor are 4, 9 and 10

What is unknown?

The smallest square that is divisible by 4, 9 and 10.

Reasoning:

The number that will be perfectly divisible by each one of the numbers is their $$LCM$$.

Steps:

\begin{align}&2\left| \!{\underline {\,{4,9,10} \,}} \right. \\&2\left| \!{\underline {\,{2,9,5} \,}} \right. \\&3\left| \!{\underline {\,{1,9,5} \,}} \right. \\&3\left| \!{\underline {\,{1,3,5} \,}} \right. \\&5\left| \!{\underline {\,{1,1,5} \,}} \right. \\&1\left| \!{\underline {\,{1,1,1} \,}} \right. \end{align}

$$LCM$$ of $$4,9,10$$
\begin{align}& =\text{ }2\times ~2\times 3\times 3~\times 5 \\& =\text{ }180 \\ \end{align}

Hence, number $$5$$ does not have a pair. Therefore $$180$$ is multiplied by $$5$$ then the number obtained is a perfect square. Therefore, $$180~\times 5\text{ }=\text{ }900$$

So, $$900$$ is the smallest square that is divisible by $$4$$, $$9$$ and $$10$$.

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