There is no definition - real or otherwise - because there can be 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.
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There are none because there is no such thing as a Greatest Common Multiple (GCM). If {a, b, c, ... x} is any set of integers, then a*b*c*...*x is a common multiple. Then twice that number is also a common multiple and is greater. And then, twice THAT number is a common multiple and greater still. It is easy to show that this process can go on for ever and so there is no such thing as a GCM.
Adding or subtracting fractions requires the use of a common multiple. It is rare that the LEAST common multiple is required - it is useful to keep the numbers small and manageable.
Well, honey, the least common multiple of 64 and 7 is 448. It's the smallest multiple that both 64 and 7 can divide into evenly. So, there you have it, darling. Math can be a real hoot sometimes!
When reducing fractions to their simplest form the greatest common factor of their numerator and denominator must be found.
The common multiples of 21 and 28 are 84, 168, 252, 336, ... and so on, never ending; so there is no real Highest Common Multiple.Do you mean:Highest Common Factor - the highest number which divides both 21 and 28 which is 7; orLowest Common Multiple - the lowest number which is a multiple of both 21 and 28 which is 84.