Can I give the Zakah to my brothers? One wants to get married these days and he will live separately. The other is younger than I, without work or income and he lives with my parents and me.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

There is no objection to give Zakah to your needy brothers, since near relatives are worthier to receive any form of good deed.
The Prophet (Sallallahu Alaihi wa Sallam) said: "Sadaqa (charity) that is given to a needy person will be rewarded as Sadaqa, but in the case of a relative it is considered as two: one reward for blood tie and the other reward for the Sadaqa itself" . A sound Hadith reported by Imam Ahmad and others.
Allah knows best.