The greatest common multiple is an infinite amount and not very practical for problem solving.
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There is no greatest common multiples for whatever common multiple is claimed to be the greatest the lowest common multiple of the numbers (in this case 15) can be added to get an even greater common multiple.
Least common multiple of 5 and 12 and 13 is 780.
The least common multiple of the numbers 5, 13 and 22 is 1,430.
The greatest common multiple is an infinite amount and not very practical for problem solving.
The greatest common denominator, like the greatest common multiple, is infinite.