Why Buddhist worship Mount Kailash? In Hinduism it is said to be the place of Lord Shiva and his wife godess parvati, How is it related to Buddhist?

Did Buddha himself ever said the importance of Mount Kailash? and if it is just a culture Buddhist follows how did it start?

Jain's are also worshipping this sacred mountain.

Buddhist Monk Milarepa have climbed Mount Kailash(is it true?)
It is in the region around Mt. Kailash that Pacceka Buddhas will reside at a time just before a Supreme Buddha is born to this world.  That is when the eminent coming of a Supreme Buddha is talked about amongst the general population of that time. 

So Mt. Kailash is a very storied mountain, the equally storied lake and the storied flower in it. Mt. Kailash is the mythical Mt. Meru. Read about it in the "Saptha Suryodgamana Sutta" The Sermon of the Seven Suns (Anguttara Nikaya VII. 62). In it the Buddha explains in detail about the events that would unfold, and in it, this monarch of mountains will get consumed and burnt, that neither ashes not soot will remain.

The Lake Anavatapta is said to be so sheltered and covered that the direct rays from the sun would not fall and the lake would not dry up until the day this world would come to an end, as per the Saptha Suryodgamana Sutta. In this "Sermon of the Seven Suns" the Supreme Buddha, tells us about the end of the earth due to the expansion of the dying sun.

To tell you a bit about the storied flower that is found in its forest…. It is the Kadupul flower - said to be the world’s most expensive flower. It survives around the Lake Anavatapta, because it is sheltered from the sun’s rays. The flower is said to be a midnight miracle, surviving during the night, and fading to nothing at dawn.