There is really no such thing as a "greatest common multiple". Once you find the least common multiple of a set of numbers, you can keep adding the LCM to itself over and over again. Each new number you get will be a common multiple of your set of numbers, but each new number will always be larger than the previous. This means that you can keep adding while the number approaches infinity and you will still never find a greatest multiple.Besides, the word "common" implies that the multiple is common to two or more numbers. There is only one in the question.
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Least Common Multiple (LCM) for 240 270 is 2,160.
least common multiple of 240 and 324 is 6480.
The Least Common Multiple (LCM) for 240 900 is 3,600.
The greatest common FACTOR of 90 and 108 is 18. The LEAST common multiple is 540. There can be no greatest common multiple since double that number will be a greater common multiple.
The greatest common multiple of any set of integers is infinite.