Multiple (mathematics)

A multiple is a term used in arithmetic, primarily due to the multiplication of integers ( ) refers. However, it can be generalized to arbitrary abelian groups. In fractional arithmetic and number theory, the least common multiples plays a role of two or more whole numbers.

Multiple of an integer

An integer is called a multiple of a number if there is an integer, so is that. In this case, is a divisor of. From a proper multiples is used when is.

Similarly, the multiple used for rational or real numbers and.

Examples

• 9 and 6 are real multiples of 3
• 6 is a proper multiple of 2
• 0 is a multiple of each number.

Multiples in abelian groups

Be an abelian group, then there exists for every one by clearly defined group homomorphism. For this

Now

For and set is called a multiple or more precisely n times of the abelian group.