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It is a negative multiple of x.It is a negative multiple of x.It is a negative multiple of x.It is a negative multiple of x.
There can be no HCM (Highest Common Multiple). Suppose x is the HCM of two numbers a and b. That is to say, x is a multiple of a, x is a multiple of b and x is the highest such number. Now consider the number 2x. It is a multiple of a, it is a multiple of b and it is greater than x. This contradicts the statement that x is the highest such number. So such an x cannot exist.
I do it like this: -- The first multiple of 8 is 8. That's not a multiple of 12. -- The second multiple of 8 is 16. That's not a multiple of 12. -- The third multiple of 8 is 24. That IS a multiple of 12, and it's the first one we ran into. or -- The first multiple of 12 is 12. That's not a multiple of 8. -- The second multiple of 12 is 24. That IS a multiple of 8, and it's the first one we ran into.
The greatest common multiple of any set of multiples is infinite.
There can be no greatest denominator. Suppose x is the greatest denominator of two numbers a and b. That is to say, x is a multiple of a, x is a multiple of b and x is the greatest such number. Now consider the number 2x. It is a multiple of a, it is a multiple of b and it is greater than x. This contradicts the statement that x is the greatest such number. So such an x cannot exist.