arithmetic – Find the smallest insertable number

Let’s say a number $$n$$ is insertable if for every digit $$d$$, if we insert $$d$$ between any two digits of $$n$$, then the obtained number if a multiple of $$d$$.
For example, $$144$$ is not insertable because $$1474$$ is not divisible by $$7$$.

The question is the find the smallest insertable positive integer with at least two digits.

It is relatively easy to see that such a number have to be divisible by $$2520$$. I also ran a script to check all integers below 75,000,000,000 with no success.

Disclaimer. I do not know if such a number do exist.