Question

What are all the multiples of $7$ and $2$ ?

Answer 1

Hint: Here we are finding all the multiples of$7$and $2$ . On multiplying a number by counting numbers, gives us its multiples.

Complete step-by-step solution:
A multiple of $7$ is a number that can be divided by $7$ leaves the remainder zero and multiples of $7$ are the product of $7$ and natural numbers.
Similarly for the number $2$ is a number that can be divided by $2$ leaves the remainder zero and multiples of $2$ are the product of $2$ and natural numbers.
Here we are going to find common multiples of the numbers that list both $7$ and $2$ as factors.
Since both $7$ and $2$ are prime so there is no need to find what their factors are. They have the factors $1$ and themselves.
And so the quick way to find a multiple of $7$ and $2$ is to multiply them.
$ \Rightarrow 7 \times 2 = 14$
We can now multiply $14$ by any number and get another common multiple of $7$and $2$.
For instance, if we multiply by $3$ we get,
$14 \times 3 = 42$
This is also a multiplier of the number $7$ and $2$.
Proceeding like this way , we need both a $7$ and $2$ in the factor tree, making them common factors.

Note:
> A number can have an infinite number of multiples. Therefore, any two numbers or set of numbers can have the infinite number of common multiples.
> The smallest common multiple of two or more numbers is called their least common multiple.
>In this problem Common multiple should be even as both will satisfy them. Common multiple should be greater than or equal to $14$ as other than that both $7$ and $2$ won’t satisfy that multiple