Find Highest Common Factors And Lowest Common Multiples

In this activity, we'll get to grips with finding the highest common factor and lowest common multiple.

But first, let's have a look at what we mean by the word factor and multiple.

 

A number that divides exactly into another number with no remainders is called a factor of that number. 

For example, to make 15 we can do 1 x 15  or  3 x 5  so the list of factors are 1, 3, 5 and 15. 

 

 

 

The highest common factor for a set of numbers is found by identifying the common factor with the highest value.

  Let's find the highest common factor for 15 and 20.   

The factors for 15 are 1, 3, 5 and 15  and the factors for 20 are 1, 2, 4, 5, 10 and 20 

The highest common factor of 15 and 20 is 5. 

 

 

A multiple is a number that is divisible by another number without leaving a remainder.

For example, 15 is a multiple of 5. You can also think of it as 'is 15 in the 5 times table?'

Multiples of 5 are 5, 10, 15, 20.. and so on.

Multiples of 3 are 3, 6, 9, 12... and so on. 

 

The lowest common multiple of a set of numbers is found by identifying the multiple which they have in common with the lowest value. 

For example, to find the lowest common multiple of 2 and 5. 

Step 1: Write down the multiples of 2 and 5.

2, 4, 6, 8, 10, 12..

5, 10, 15, 20, 25..

Step 2: Identify the smallest multiple which they have in common.

That would be  10!

 

 

Are you ready to try some questions now?