# EdPlace's Year 7 home learning maths lesson: HCF and LCM

Looking for short lessons to keep your child engaged and learning? Our experienced team of teachers have created English, maths and science lessons for the home, so your child can learn no matter where they are. And, as all activities are self-marked, you really can encourage your child to be an independent learner.

**Get them started on the lesson below **and then jump **into our teacher-created activities** to practice what they've learnt. We've recommended five to ensure they feel secure in their knowledge - 5-a-day helps keeps the learning loss at bay (or so we think!).

Are they keen to start practising straight away?** Head to the bottom of the page to find the activities. **

**Now...onto the lesson!**

**Key Stage 3 Statutory Requirements for Maths**

**Year 7**

*students should be able to use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor, lowest common multiple, [and] prime factorisation.*

# What's It All About?

This guide will explain how to cover** highest common factor** (**HCF**) and **lowest common multiple** (**LCM**). There are many definitions that need remembering, so this will include ways of understanding the key vocabulary, as well as the methods required to find **LCM** and **HCF**. ** **We're confident that if you follow this step-by-step approach together, your child will be able to:

1) **Write** a number as a product of prime factors.

2) **Find** the highest common factor of two numbers.

3) **W**** ork-out** the lowest common multiple of a pair of numbers.

## Factors and Multiples

The best way to introduce this topic is to define “**factor**” and “**multiple**”, as the two are often confused.

**Factors** are numbers that **divide** into a given number. For example, **factors** of 20 are 1, 2, 4, 5, 10, and 20. These numbers **divide** into 20 with no remainder.

**Multiples** of a number are answers we get when we **multiply** that number. (Think “multiple” and “multiply”). Another way to think of it would be: “the answers to its times table”. For example, the **multiples** of 20 are 20, 40, 60, 80, 100, and so on.

It is key that your child can tell the difference between **factors** and **multiples**.

## Prime Numbers

## Now let us move on and discuss “**prime**” **numbers**. **The definition of a prime number is a number that can only divide by itself and 1.** (In other words, **it only has two factors**; it is not a solution in any times tables). For instance, 7 is a **prime number** because its only **factors** are 1 and 7. Meanwhile, 20 is not **prime**, because as we saw in Step 1, it has more than two **factors**.

An important point here is **1** is **not** a **prime number**. This is because it only has one **factor** (which is itself!), not two.

## Step 1- Factor Tree's

Once you understand** prime numbers**, you should be able to **write a number as the product of its prime factors. **This is quite a common question that you can be tested on, and sounds complicated, but all you need to do is** keep dividing the number up until you reach prime numbers.**

For example, if we want to write 180 as the product of **prime factors**, we draw a “**factor tree**” and split the number up by **dividing** it as far as we can. Every **pair** of “branches” represents a pair of numbers that **multiply** together to make the number above it.

We have **divided** 180 as far as we can take it. The 2s, 3s, and 5 cannot have any branches added because they are** prime.**

**So, as the product of its prime factors, 180 = 2 x 2 x 3 x 3 x 5. **

## Step 2 - Highest Common Factor

This leads us to finding the **highest common factor **(**HCF**) of two numbers.

All we need to do is make two “**factor trees”** as we saw in Step 1, then see what numbers occur at the end of both trees.

For example, let us find the **HCF** of 180 and 108 by drawing both trees:

All we need to do now is circle all the numbers that appear in both lists, and then **multiply** them.

As we can see, these trees share a pair of 2s and a pair of 3s, so the **HCF** is 2 x 2 x 3 x 3 = 36.

## Step 3 - Lowest Common Multiple

Finally, we will look at how to find the **lowest common multiple** (**LCM**) of two numbers.

As we considered in the **Factors and Multiples **segment, **multiples** are the solutions to times tables, so the easiest way to find the **LCM** is to **list both times tables** until you **reach the same number** in both lists.

For example, if we want the **LCM** of 9 and 12:

**Multiples** of 9 = 9, 18, 27, **36**, 45, …

**Multiples** of 12 = 12, 24, **36**, 48, …

**36** is the first number to appear in both lists, so that is the LCM.

## Step 4 - Putting it into Practice

1) Write down all the **prime numbers** between 1 and 10.

2) Write 84 as a product of its **prime factors**.

3) Work out the **LCM** of 12 and 20

4) Work out the **HCF** of 24 and 36

5) Cans of lemonade are sold in packs of 6. Cans of cola are sold in packs of 4. You want the same amount of each drink. What is the minimum number of drinks you need to buy?

## Step 5 - Give it a go...

Why not test your child's understanding and see if they can tackle these activities?

All activities are **created by teachers and automatically marked.** Plus, with an EdPlace subscription, we can **automatically progress your child** at a level that's right for them. Sending you progress reports along the way so you can **track and measure progress, together** - brilliant!

Activity 1 - Highest Common Factor (1)

Activity 2 - Highest Common Factor (2)

Activity 3 - Lowest Common Multiples (1)

Activity 4 - Lowest Common Multiples (2)

Activity 5 - Lowest Common Multiples (3)

**Answers**

1) The **prime numbers** are 2, 3, 5, 7.

2) 84 = 7 x 3 x 2 x 2

3) By listing both times tables:

12, 24, 36, 48, 60

20, 40, 60

**LCM** = 60

4) If we draw both **factor trees** we would find:

24 = 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

These share a pair of 2s and one 3, so if we **multiply**, the **HCF** is 2 x 2 x 3 = 12.

5) Questions like this are **LCM.** The **lowest common multiple** of 4 and 6 is 12. So you would buy 12 cans of each drink.

Keep going! Looking for more activities, different subjects or year groups?

Click the button below to view the EdPlace English, maths, science and 11+ activity library