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There can never be a greatest common multiple of one number for two reasons:

  1. "Common" refers to a multiple that is common to two or more numbers. You cannot have a multiple that is common, but only to one number.
  2. If X is the greatest common multiple of a set of numbers, then any multiple of X will also be a common multiple of each member of the set and it will be greater than X. And then, any multiple of this number will be a multiple of each member of the set and will be greater still. And then ...
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7y ago

The greatest common multiple of any set of integers is infinite.

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Q: What is the greatest common multiple of 7?
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The greatest common multiple of any set of integers is infinite.--------------------------------------------------------------------------------------------------------Did you perhaps mean:the greatest common FACTOR (the greatest number which divides into 14 and 21 without remainder): gcf(14, 21) = 7;the LOWEST common multiple (the smallest number which is a positive multiple of both 14 and 21): lcm(14, 21) = 42


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