Do I only need one swap partition for multiple Linux distros? (and other questions)

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http://unix.stackexchange.com – I have Linux Mint 14 installed as my only OS. I have one extended partition containing /swap, / and /home, and I have some unallocated space on my drive. I'm guessing that Mint decided to put this all on an extended partition instead of three primary partitions. So I want to build Linux From Scratch using some of my unallocated space. My first question is, do I need to have a swap partition for each distro or can LFS use the swap partition I already have? If so, would the swap partition have to be a primary partition, or does it not matter? Is there any practical difference between a (HowTos)