But Who Ate The Most?

Five brothers stayed in the house with their mother. One day, their mother brought home some mangos.

Alex woke up first. As he was hungry, he ate \( \frac{1}{6} \) of the mangoes, and headed out.
Brian woke up next. As he was hungry, he ate \( \frac{1}{5} \) of what was left, and headed out.
Charles woke up next. As he was hungry, he ate \( \frac{1}{4} \) of what was left, and headed out.
Danny woke up next. As he was hungry, he ate \( \frac{1}{3} \) of what was left, and headed out.
Euler woke up next. As he was hungry, he ate \( \frac{1}{2} \) of what was left, and headed out.

Their mother came home and saw 3 mangoes in the basket. How many mangoes were there initially?