Write any five three digit numbers which are multiples of $2$.

Hint: We first find the ranges for the five three-digit numbers and then we use the condition for the numbers to be divisible by 2 is even numbers. Finally, we find the 5 even numbers in between 100 and 999.

Complete step by step solution:
We have to find five three-digit numbers which are multiples of $2$.
The range of the three-digit numbers is from 100 to 999.
Every even number is divisible by $2$. So, we have to find $5$ even numbers between 100 and 999.
Let us take $232, 458, 576, 764, 994.$
We now just need to check if the numbers are divisible by 2.
\[\begin{align}
  & 232=2\times 116 \\
 & 458=2\times 229 \\
 & 576=2\times 288 \\
 & 764=2\times 382 \\
 & 994=2\times 497 \\
\end{align}\]
All the numbers 232, 458, 576, 764, 994 are multiple of 2.
Therefore, five three-digit numbers which are multiples of 2 are $232, 458, 576, 764, 994$.

Note: We can also take 5 consecutives even numbers where the difference between the numbers will be 2. There are many three digit numbers which are multiple of 2 but in above we took them randomly. We can also show the division form of the numbers to find the multiplier.