 # Find the Lowest Common Multiple (LCM)

In this worksheet, students will find the LCMs of pairs of numbers by listing their multiples and finding the lowest multiple which appears in both. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Number Operations and Integers

Curriculum subtopic:   Structure and Calculation, Whole Number Theory

Difficulty level:   ### QUESTION 1 of 10

Hopefully you know how to find a multiple of a number.

To remind you, a multiple of a number just refers to the answers you reach when you use this number as the multiplier.

e.g.

The multiples of 5 would be: 5, 10, 15, 20, etc.

The multiples of 7 would be 7, 14, 21, 28, 35, etc.

The Lowest Common Multiple (LCM) is an extension of this concept, but involves more than one number.

The LCM of two numbers is: The first number which appears in the times table for two (or more) numbers.

e.g. Find the LCM of 6 and 9.

Firstly, we need to list the multiples of both numbers:

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

We can see that the first number which appears in both lists is 36.

This means the LCM of 6 and 9 is 36.

In this activity, you will find the LCMs of pairs of numbers by listing their multiples and finding the lowest multiple which appears in both.

You may want to have a pen and paper handy so that you can write out your lists to help you answer these questions.

Complete the blanks below to define what the acronym LCM stands for.

What is the LCM of 4 and 12?

What is the LCM of 8 and 12?

12

24

48

96

Which of these numbers are common multiples of 4 and 8?

4

8

16

24

32

44

What is the LCM of 7 and 7?

Match each number pair with their Lowest Common Multiple.

## Column B

7 and 10
8
3 and 4
24
8 and 12
12
2 and 8
70

The LCM can be found by multiplying the two numbers together.

In what circumstances is the statement above true?

Always

Sometimes

Never

What will the LCM of 1 and any other number always be?

1

The other number

What is the LCM of 24 and 40?

Complete the sentence below to summarise the method you have learnt for finding LCMs.

• Question 1

Complete the blanks below to define what the acronym LCM stands for.

EDDIE SAYS
We'll be using the phrase LCM throughout this activity. You will need to remember that it stands for:

Lowest Common Multiple

This means the smallest multiple which appears in the times tables of two (or more) numbers. Let's put this into practise now in the rest of this activity.
• Question 2

What is the LCM of 4 and 12?

12
EDDIE SAYS
As we discussed in the Introduction, the first step is to write out the times tables or multiples of each number: 4: 4, 8, 12, 16, 20, 24, etc. 12: 12, 24, 36, 48, 60, 72, etc. The LCM will be the first number that appears in both lists. In this case, this is 12.
• Question 3

What is the LCM of 8 and 12?

24
EDDIE SAYS
A common mistake is just to multiply the two numbers together (8 x 12 = 96). This gives you a common multiple, but it isn't the lowest common multiple To get the lowest answer, we need to list the multiples of 8 and 12 to find the first number that appears in both. 8: 8, 16, 24, 32, 40, etc. 12: 12, 24, 36, 48, 60, etc. 24 is the LCM of 8 and 12, as it is the first multiple which appears in both lists.
• Question 4

Which of these numbers are common multiples of 4 and 8?

8
16
24
32
EDDIE SAYS
Make sure that you read the questions fully. This question doesn't ask for the lowest common multiple; it just asks for the common multiples. These can be identified in exactly the same way as the LCM. Write out the multiple lists and then find all the numbers which appear in both lists, rather than just the lowest. 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, etc. 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, etc. Great focus, let's continue so you can practise these skills some more.
• Question 5

What is the LCM of 7 and 7?

7
EDDIE SAYS
The LCM is the first number that appears in times tables for two or more numbers. What is the first number that is in both times tables, if the numbers are the same? That's correct, it's the number itself. Remember this fact moving forwards so you can save time on questions of this type.
• Question 6

Match each number pair with their Lowest Common Multiple.

## Column B

7 and 10
70
3 and 4
12
8 and 12
24
2 and 8
8
EDDIE SAYS
This question is making a point about a misconception. Don't, whatever you do, assume that multiplying the numbers together will give the LCM. The only way to make sure you find the LCM is to use the listing method to ensure you find the common multiple with the lowest value. For example, the list for the first pair are: 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, etc. 10: 10, 20, 30, 40 50, 60, 70, 80, 90, 100, etc. The first number which appears in both list is 70, so this is the LCM of this pair. Follow this pattern to find the LCM of the other pairs.
• Question 7

The LCM can be found by multiplying the two numbers together.

In what circumstances is the statement above true?

Sometimes
EDDIE SAYS
This method will work for some pairs (e.g. 3 and 4) but not for others (e.g. 6 and 10). It would be an error to assume that this is always going to be a shortcut to the correct answer, but it can be helpful to commit the common pairs to memory where this approach does work. The only way to calculate the LCM accurately for all number pairs or sets is to write out the list of multiples, and find the smallest multiple they have in common.
• Question 8

What will the LCM of 1 and any other number always be?

The other number
EDDIE SAYS
Don't get caught out with questions like this! Every integer is in the 1 times tables, so the unknown number must also be in that list. This means that the first number in the unknown number's times table must also be in the 1 times table. As 1 is the smallest integer, it stands to reason unless the unknown number is 1 too, every other number will be of higher value. Therefore, the LCM will be based on the value of the unknown number, not 1.
• Question 9

What is the LCM of 24 and 40?

120
EDDIE SAYS
Even though the numbers are bigger, the method here is the same. Let's make our two lists: 24: 24, 48, 72, 96, 120, 144, etc. 40: 40, 80, 120, 160, 200, 240, etc. What's the first multiple to appear in both times tables?
• Question 10

Complete the sentence below to summarise the method you have learnt for finding LCMs.

EDDIE SAYS
This question reinforces the message about how to find the LCM: - List both sets of multiples; - Find the smallest or first number which appears in both lists. If you follow this process then you can't go wrong, and will find the correct LCM every time!
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