1 Master -> Many slaves, need to update dump file

[Brian Wright]

We have a MySQL setup with 1 Master server and many slaves for distributed statistics gathering (That I inherited and am definitely not a MySQL expert). We occasionally deploy new slaves to keep up with the demand. When the replication was first setup, there was the initial dump file created with mysqldump, then the SHOW MASTER STATUS was used to get the binlog file and position to configure the slaves with. The disk space is starting to fill up with the binlog files (there is currently no automatic maintenance to purge them). Also deploying new servers takes 10-12 hours for replication to catch up, so I want to create a new dump file to shorten this time.

I need some assistance with regards to purging the binlog files, creating a new master dump file, and not breaking the existing slave replication. The current slaves are using the binlog file name and position from the initial dump file. If I lock the tables to do a new dump, then purge the existing binlog files, will the current slaves have any replication issues? What is the best practices for doing something like this?

Thanks in advance!

-Brian