Kim Kardashian and sister Kourtney Kardashian appeared on "The Late Show with David Letterman" on Wednesday, Jan. 16,  to promote the premiere of "Kourtney & Kim Take Miami."

Letterman cracked several jokes about Kim's marriage, which led to her firing back at him and then later her older sister Kourtney did the same. Kim called him out when she said in a serious tone that "those jokes really can't work, because I've really been married for almost two years. . . . So it hasn't been 72 days, it's been almost two years."

Kim and NBA player Kris Humphries tied the knot in August of 2011, with Kim filing divorce papers on Oct. 31.

Kim then explained to Letterman that she "would love" to get an divorce from Humphries, 28, but he is requesting an annulment to accuse her of defrauding him by marrying him for publicity, not love. Read the excerpt from the interview below:

Letterman: "Now, you're still married to the former husband, Kris Humphries? You're still married to him?" 

Kim: "Yes, I am."

Letterman: "Now, when are you going to wrap that up?"

Kim: "Well, I'm trying, and it's a process...I've been trying for almost two years now, um, to wrap it up, but it's, you know, it's hard."

Letterman: "What does Mr. Humphries - I guess it's none of my business - but what does he want? Does he want his own show?"

Kim: "I can't speak for Kris, but I just want him to be happy and I want us to move on, and that's really what I want, is just to move on."

Letterman: "...When the divorce comes through - and he wants an annulment, is that right?"

Kim: "Yes."

Letterman: "...Why an annulment? What's the difference here?"

Kim: "I don't really know 'cause even if we got an annulment - I would love to give him one but then that would make - the only legal way to get an annulment is if fraud were involved, so that's what tricky. So he is suing me for an annulment based on the fact that I frauded him into marrying him for publicity."

Letterman: "Oh, so he's claiming that he was the victim of fraud."

Kim: "Yes, well, that's the only way to get an annulment is if one person was frauded, so that was the case."

Letterman: "But fraud was not a factor here, is that right?"

Kim: "Not in my case, no."

Then Kourtney defended her younger sister when she said, "But I think if she was going to do it for publicity, she'd pick someone that people knew."

"Wow - ouch!" Letterman replied then laughed.

"Kourtney & Kim Take Miami" will premiere on E! on Sunday, Jan. 20, at 9 p.m. EST.

Watch the video clip below where Kourtney defends her younger sister Kim on "The Late Show With David Letterman."

Tags: kourtney kardashian Kim Kardashian David Letterman Kris Humphries