Question

What are two multiples that 4 and 8 have in common?

Answer 1

Hint: Multiples are the product of a given number with an integer. First we will find the multiples of 4 and 8 individually. Then, to find the common multiples, we will compare the multiples of both. This comparison will get us the required answer.

Complete step by step solution:
We have been given two numbers 4 and 8.
We have to find the common multiples of both 4 and 8.
Now, we know that Multiples are the product of a given number with an integer.
First we will obtain the multiples of 4 by multiplying the 4 by another whole number. Then we will get
Multiples of 4 $\Rightarrow 4=\left\{ 4,8,12,16,20,24,28....... \right\}$
Now, let us obtain the multiples of 8 by multiplying the 8 by another whole number. Then we will get
Multiples of 8 $\Rightarrow 8=\left\{ 8,16,24,32,40,....... \right\}$
Now, we know that the multiple of any number must be greater than or equal to that number.
Now, we will find that the common multiples of 4 and 8 will be
$\Rightarrow \left\{ 8,16,24,....... \right\}$
Hence we get the common multiples of 4 and 8.

Note: The confusion arises between factors and multiples but both are different. Factors of a number are those numbers which divide the given number completely without leaving remainder. A number has an infinite number of multiples. Zero is the multiple of every number but zero is not a factor of any number.