Prepare water bath canner, jars and lids. Wash jars and bands with hot, soapy water, then place in water bath canner and bring water to a simmer to sterilize jars. Leave jars in canner until ready to fill. Always use new lids when canning (bands can be reused).
Peel and core the pineapples. **Save the cores
Chop the pineapple into chunks. Large hunks, small chunks or minced for crushed pineapple. Choose your preference.
In a large, stainless steel pot, simmer the chopped pineapple cores in water for about 10 minutes, and then strain out the cores. Reduce heat to medium low.
Add pineapple chunks to liquid. Heat thoroughly (about 30 seconds per pound).
Use a slotted spoon to pack hot pineapple chunks into jars, leaving a generous ½ inch headspace. Then ladle hot syrup into jars, covering pineapple chunks, leaving ½ inch headspace.
Remove any air bubbles by running a butter knife along the inside of the jar. Adjust headspace if necessary. Wipe rim, place lids on top, screw bands on and place in the canner, ensuring that jars are completely submerged in water.
Bring water to a boil and process pint jars for 15 minutes or quart jars for 20 minutes. Once time is up, turn heat off, remove canner lid, let sit for 5 minutes and then remove and let cool completely before storing in a cool, dark place.