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Q: Are any of the numbers 91 834 and 560 a multiple of 7?

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Any number of the form 560*k where k is an integer.

Any multiple of 40.

Any multiple of 2520.

Any multiple of 4.

Any multiple of 36.

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Any number of the form 560*k where k is an integer.

The greatest common multiple of any set of numbers is infinite. The greatest common multiple of any set of numbers will never be one.

1 is only a multiple of itself.

The greatest common multiple of any two numbers is infinite.

Any multiple of 40.

There is no greatest common multiple of these numbers... or indeed of any pair of numbers. Once you get a common multiple, you can multiply that by any integer, as large as you want, to get a larger common multiple.

Their least common multiple (or their product - any multiple will do), and any multiple of that.

Yes.

any multiple of 7

Any multiple of 2520.

Any multiple of 4.

There is really 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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