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# A number when divided by $9$ gives the perfect cube of $6$ and when multiplied by $3$ gives another perfect cube of $18$. Find the number.

**Given:**A number when divided by $9$ gives the perfect cube of $6$ and when multiplied by $3$ gives another perfect cube of $18$.

**To do:**To find the number.

**Solution:**

Let $x$ be the number.

As given, when the number is divided by $9$ gives the perfect cube of $6$

$\Rightarrow \frac{x}{9}=6^3=6\times6\times6=216$

$\Rightarrow x=216\times9$

$\Rightarrow x=1944$

If we multiply the number by $3$, it becomes the cube of $18$.

$\Rightarrow 3x=18^3=18\times18\times18=5832$

$\Rightarrow x=\frac{5832}{3}$

$x=1944$

Therefore, $x=1,944$.

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