Day of Lailat-al Qadr

Almost every Muslim child knows that `Lailatul Qadr is 27th of Ramadan. But when they grow up, some of them try to know more and conclude that Lailatul Qadr` can take place at any day of Ramadan. Growing some more, I listened that `Lailatul Qadr can take place at any day of the year, not only in Ramadan. What is the true fact? Can Lailatul Qadr take place without Ramadan`? Please describe with evidence. Jajakallah.