In the play Macbeth By William Shakespeare who is responsible for the death of duncan and why?

In the play Macbeth by William Shakespeare , Macbeth finds out he can become king from 3 witches and then tells his wife lady macbeth that he could become king in a letter and she then convinces him to kill the king in order to become king. Macbeth then kills Duncan the King, who is responsible for this - the witches for telling Macbeth he could be king, the Macbeth for killing him or Lady Macbeth for convincing Macbeth to do it ?