Identify multiples of a number

A multiple of a positive whole number $n$ is a product $n \times k$ , where $k$ is a whole number, forming the sequence $0,n,2n,3n,\ldots$ . Identifying multiples involves recognizing these patterns through multiplication, skip-counting, or number-line spacing and determining whether a given whole number can be written as $n \times k$ ; this distinguishes multiples from factors and supports divisibility and common-multiple reasoning, without extending to noninteger or abstract algebraic settings.

Detailed Explanation: Identify multiples of a number

A multiple of a number is the result of multiplying that number by a whole number.

For example, the multiples of $6$ are found by multiplying $6$ by $0,1,2,3,\ldots$ :

6\times0=0,\quad 6\times1=6,\quad 6\times2=12,\quad 6\times3=18,\ldots

So the multiples of $6$ begin:

0,6,12,18,24,30,36,42,\ldots

Example

Is $42$ a multiple of $6$ ?

Ask whether $42$ can be written as $6$ times a whole number.
Divide:

42\div6=7

Since $7$ is a whole number, we can write:

42=6\times7

Therefore, $42$ is a multiple of $6$ .

You can also check by skip-counting by $6$ : $6,12,18,24,30,36,42$ . Because you land exactly on $42$ , it is a multiple of $6$ .

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Finding Lowest Common Multiple

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