Which movie had the largest Oscar sweep (winning awards in every nominated category)?
This question is really tricky and hard, as it is a well-known fact that every movie listed was outstandingly successful at the ceremony, and all three of them won 11 awards. But the thing is that only one of them won an award in every nominated category, and it was The Lord of the Rings: The Return of the King (2003).
Titanic (1997) had 14 nominations and Ben-Hur (1959) had 12. Titanic lost Best Actress in a Leading Role (Kate Winslet), Best Actress in a Supporting Role (Gloria Stuart), and Best Makeup. Ben-Hur missed for Best Writing, Screenplay Based on Material from Another Medium
The Lord of the Rings: The Return of the King (2003) won all 11 categories for which it was nominated: Best Picture, Director, Adapted Screenplay, Original Score, Original Song, Sound Mixing, Art Direction, Makeup, Costume Design, Film Editing, and Visual Effects.