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Jess Davies
14/12/2025
Maths
HCF and LCM
73
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14 Dec 2025
•
Understanding HCF and LCM: Step-by-Step Guide
Jess Davies
@jess_notes21
1 / 3
Understanding Prime Factors and Factor Trees
Prime numbers are the building blocks of all numbers - they only divide by themselves and 1 (like 2, 3, 5, 7, 11). Think of them as mathematical atoms that can't be broken down further.
A prime factor tree helps you break any number down into these basic building blocks. For example, to find the prime factors of 72, you keep dividing until you're left with only prime numbers.
Starting with 72, you might divide by 8 and 9, then break those down further until you get 72 = 3 × 3 × 2 × 2 × 2. In index form, this becomes 3² × 2³, which is much tidier to write.
Quick Tip: Always start your factor tree with any factors you can spot easily - there's no single "correct" way to draw it, as long as you end up with prime numbers at the bottom!
Finding HCF and LCM Using Prime Factors
The highest common factor (HCF) is the biggest number that divides into both your numbers exactly. The lowest common multiple (LCM) is the smallest number that both your original numbers divide into.
Let's work through finding the HCF and LCM of 36 and 56. First, break both numbers into their prime factors using factor trees: 36 = 3 × 3 × 2 × 2 and 56 = 7 × 2 × 2 × 2.
Now comes the clever bit - draw a Venn diagram with two overlapping circles. Put the prime factors that appear in both numbers (the common ones) in the overlapping section.
Remember: The Venn diagram method makes it impossible to get HCF and LCM mixed up - you'll never confuse which calculation to use!
Calculating Your Final Answers
For 36 and 56, the common prime factors are 2 × 2, so these go in the overlapping section of your Venn diagram. The remaining factors (3 × 3 for 36, and 7 × 2 for 56) go in the outer parts of each circle.
The HCF is simply the product of everything in the overlap: 2 × 2 = 4. This means 4 is the largest number that divides exactly into both 36 and 56.
The LCM uses every prime factor exactly once, so multiply everything across both circles: 3 × 3 × 2 × 2 × 2 × 7 = 504. This means 504 is the smallest number that both 36 and 56 divide into exactly.
Pro Tip: You can check your LCM by verifying that both original numbers divide into it exactly - 504 ÷ 36 = 14 and 504 ÷ 56 = 9, both with no remainders!
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This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
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very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
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I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
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This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
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Understanding HCF and LCM: Step-by-Step Guide
Jess Davies
@jess_notes21
Ever wondered how to find what numbers have in common or their smallest shared multiple? Understanding HCF and LCM is crucial for solving fraction problems, simplifying expressions, and tackling exam questions with confidence.
Understanding Prime Factors and Factor Trees
Prime numbers are the building blocks of all numbers - they only divide by themselves and 1 (like 2, 3, 5, 7, 11). Think of them as mathematical atoms that can't be broken down further.
A prime factor tree helps you break any number down into these basic building blocks. For example, to find the prime factors of 72, you keep dividing until you're left with only prime numbers.
Starting with 72, you might divide by 8 and 9, then break those down further until you get 72 = 3 × 3 × 2 × 2 × 2. In index form, this becomes 3² × 2³, which is much tidier to write.
Quick Tip: Always start your factor tree with any factors you can spot easily - there's no single "correct" way to draw it, as long as you end up with prime numbers at the bottom!
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Finding HCF and LCM Using Prime Factors
The highest common factor (HCF) is the biggest number that divides into both your numbers exactly. The lowest common multiple (LCM) is the smallest number that both your original numbers divide into.
Let's work through finding the HCF and LCM of 36 and 56. First, break both numbers into their prime factors using factor trees: 36 = 3 × 3 × 2 × 2 and 56 = 7 × 2 × 2 × 2.
Now comes the clever bit - draw a Venn diagram with two overlapping circles. Put the prime factors that appear in both numbers (the common ones) in the overlapping section.
Remember: The Venn diagram method makes it impossible to get HCF and LCM mixed up - you'll never confuse which calculation to use!
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Calculating Your Final Answers
For 36 and 56, the common prime factors are 2 × 2, so these go in the overlapping section of your Venn diagram. The remaining factors (3 × 3 for 36, and 7 × 2 for 56) go in the outer parts of each circle.
The HCF is simply the product of everything in the overlap: 2 × 2 = 4. This means 4 is the largest number that divides exactly into both 36 and 56.
The LCM uses every prime factor exactly once, so multiply everything across both circles: 3 × 3 × 2 × 2 × 2 × 7 = 504. This means 504 is the smallest number that both 36 and 56 divide into exactly.
Pro Tip: You can check your LCM by verifying that both original numbers divide into it exactly - 504 ÷ 36 = 14 and 504 ÷ 56 = 9, both with no remainders!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user