There is no highest common multiple. Once you get a common multiple - for example, multiplying 18 x 57, or using prime factorization to get the smallest common multiple - you can multiply it by 2, by 3, by 4, etc. and get ever-larger common multiples.
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The Greatest Common Denominator is 6
There can be no greatest common denominator. If you have a set a numbers whose least common denominator is L then 2*L, 3*L, … are all common denominators. There is no end to that sequence and so no greatest.
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The greatest common denominator of any set of integers is infinite.