Q: What is the definition of a multiple of a number?

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Multiplication

That's the definition of a multiple.

A multiple of 3 is a number evenly divisible by 3.

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.

No.3 is less than 5, thus cannot be a multiple of it; 3 is prime, therefore cannot be a multiple of any number besides 3 (which is one of its factors); by definition, 3 is ismply not a multiple of any number but 1 and 3.

Related questions

An odd number

A number that can be divided by another number without a remainder.

Multiplication

That's the definition of a multiple.

You could say that a prime number is also a multiple of 1. A good definition of prime number is: "a natural number with exactly two distinct factors". This definition explains why 1 is not a prime number.

By definition a prime number is divisible only by itself and 1, so it can't be a multiple of any other number.

A number that contains another number an integral number of times without a remainder

That's the definition of a multiple.

If you mean "each of its factors", then you might say "by definition". If a number is a factor of another number, then that means that the other number is a multiple.

The definition of the greatest common multiple of any two numbers is an infinite number.

That's the definition of a multiple.

A multiple of 3 is a number evenly divisible by 3.