72

The number 72 plays a significant role in Assassin's Creed: Brotherhood. It is the password, which needs to be spoken, in order to the gain access to the Colosseum Vault.

Also, when Lucy's team of Assassins entered the Vault, there were 72 days remaining until Abstergo's launch of their satellite mounted with a Piece of Eden. Rodrigo Borgia and Maria Auditore da Firenze died at the age of 72.

Creation and Clues
Ezio discovered, or created the password in 1500's and used it to seal the Apple of Eden within the Colosseum Vault. Leonardo da Vinci, a long-time friend of Ezio's, persuaded him to leave a clue to the password behind. Desmond knew that Ezio had returned to the Villa Auditore due to a vision he had from the bleeding effect. Presumably Ezio left the password in such a way that it could only be seen in Eagle Vision, either for a fellow Assassin or descendant to find it.

In Mario's study, a bookcase conceals the entrance to a secret passageway leading down some stairs to the Sanctuary. At the top of the stairs, engraved into the wall, is an equilateral triangle. The triangle is split into nine smaller equilateral triangles. Noticing the marking on the wall, Shaun Hastings mentioned this to his fellow Assassins. Desmond then used his Eagle Vision to reveal three numbers; 1419, 1420 and 1421.

Realization
After discovering the location of the Apple through the use of the Animus 2.0, the Assassins pondered how to access the Vault.
 * Rebecca: It seems to open with a verbally triggered mechanism. I've never seen anything like it.
 * Lucy: You mean it needs a password?
 * Shaun: Try humming Beethoven's Fifth.

The power cut off, disabling the Animus so the team could no longer search Ezio's memories for the password. Desmond went back to the markings at the top the stairway and called the others. They discussed the symbol and the relevance of the numbers. The triangular symbol on the wall of the Villa Auditore matched the symbol on the door to the Vault.

Shaun discovered the password and explained to the rest of the team:

"The Tetragrammaton. The 72 name of God. You see? They're all contained within three verses. Exodus 19 through 21. And, get this, you'll like this, if you arrange the four Hebrew letters in God's name within an equilateral triangle; their numerical values add up to the same number: 72."

- Shaun Hastings explains the password to the Modern Day Assassins

They then made their way to Colosseum and Desmond, saying '72' aloud, opened the sealed door, gaining them access to both the Vault and the Apple.