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The lesser rings were forged by the elves as essays in the craft of ring making. These rings were made sometime between S.A. 1200, when Sauron came in disguise to Eregion, and 1500, when they began crafting the greater Rings of Power.
Tolkien's essay "Of the Rings of Power and the Third Age" in The Silmarillion gives the background of the making of the rings. Midway through the Second Age Sauron came in disguise as Annatar ("Lord of Gifts") to the Elven smiths of Eregion, who were led by Celebrimbor, and taught them the craft of forging magic rings. Tolkien writes that the Elves made many lesser rings as essays in the craft, but eventually with Sauron's assistance they forged the Seven and the Nine. The Three were made by Celebrimbor himself without Sauron's assistance; they remained unsullied by his touch.
What became of these lesser 'essay' rings?