A multiple of $3$ gives
$0,3,6,9,12,15,18,21,24,27$
which rearrange the last bit of each number gives $0,1,2,3,4,5,6,7,8,9$ once. The same can be said of $7$ and $9$ as well which gives
$0,7,14,21,28,35,42,49,56,63$
and
$0,9,18,27,36,45,54,63,72,81$
which give the exact number sequence backward.
I am just curious to know is there a definition for this kind number maybe a property of prime that I am unaware of?
This has to do with the fact that $1,3,7,9$ are relatively prime to $10$. Because of this, there is always a solution to $$ax \equiv d \pmod {10} \,\,\,\, (\heartsuit)$$ where $a \in \{1,3,7,9\}$ and $d \in \{0,1,2,3,\ldots,9\}$, which essentially means that there is a multiple of $a$, i.e. $x$, such that $ax$ ends with the digit $d$.
The fact there is a solution to $(\heartsuit)$, when $\gcd(a,10) = 1$ can be seen from Bezout's identity/ Euclidean algorithm. In general, the set of numbers relatively prime to $n$, called as reduced residue system, forms a group under multiplication and hence these numbers obey some nice properties.