Find the greatest $3\text{-digit}$ number exactly divisible by $18$, $24$ and $36$.

1. Find the Least Common Multiple (LCM) of $18,24,$ and $36$:
* Prime factorization:

$$18=2^1\times 3^2$$

$$24=2^3\times 3^1$$

$$36=2^2\times 3^2$$

* $\text{LCM}=2^3\times 3^2=8\times 9=72$

2. Find the greatest $3\text{-digit}$ number multiple of $72$:
The greatest $3\text{-digit}$ number is $999$. Divide it by $72$:

$$\frac{999}{72}=13\text{ with a remainder of }63$$

3. Subtract the remainder from $999$:

$$\text{Required Number}=999-63=936$$