Alyson, Clara and Joyce were each given a piece of string of equal length. Alyson cut hers into smaller $$2\text{m}$$ pieces, Clara cut hers into smaller $$3\text{m}$$ pieces, and Joyce cut hers into smaller $$5\text{m}$$ pieces. If there were no remainder in each case, find the shortest possible length of string given to each of them. 
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