Cheryl and Denise.

Cheryl and Denise were given each a positive integer from 1 to 9, and they were told that one of their numbers was a multiple of the other number. They were tasked to find out the other friend's number, by a conversation. The following conversation ensued:

Cheryl: I do not know your number. But I know that you don't know my number.

Denise: I do not know your number either. But I also know that you don't know my number.

Cheryl: I now know your number. But I know that you still don't know my number.

Denise: You're right. I still don't know your number.

If both of them were logical in their thinking process, what is Denise's number?

Hint: Go and search about the Cheryl's Birthday Problem first!