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HCF and LCM

Practise finding the highest common factor (HCF), sometimes called the greatest common divisor, and the lowest common multiple (LCM) of two numbers.

Sieve Trees Level 1 Level 2 Level 3 Level 4 Level 5 Description Help Factors Multiples

This is level 1; Finding the highest common factor (HCF) of two numbers. You can earn a trophy if you get at least 9 correct and you do this activity online.

Find the HCF of
8 and 12.

Correct Wrong

Find the HCF of
4 and 8.

Correct Wrong

Find the HCF of
3 and 4.

Correct Wrong

Find the HCF of
12 and 36.

Correct Wrong

Find the HCF of
20 and 12.

Correct Wrong

Find the HCF of
36 and 27.

Correct Wrong

Find the HCF of
38 and 95.

Correct Wrong

Find the HCF of
119 and 85.

Correct Wrong

Find the HCF of
96 and 72.

Correct Wrong

Find the HCF of
192 and 72.

Correct Wrong

Find the HCF of
27 and 23.

Correct Wrong

Find the HCF of
192 and 240.

Correct Wrong

Check

This is HCF and LCM level 1. You can also try:
Level 2 Level 3 Level 4 Level 5

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Description of Levels

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Level 1 - Finding the highest common factor (HCF) of two numbers.

Level 2 - Finding the lowest common multiple (LCM) of two numbers

Level 3 - Finding the highest common factor (HCF) of large numbers.

Level 4 - Finding the lowest common multiple (LCM) of large numbers

Level 5 - Finding the HCF and LCM of three numbers

Sieve Use the Sieve of Eratosthenes to find prime numbers.

Factor Trees An interactive and very visual way to break down a number into its prime factors.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Help

The highest common factor (HCF) of two numbers is the largest number that divides exactly into both of the numbers.

You can Find the HCF of
numbers by listing the prime factors of both numbers then multiplying together the factors that appear in both lists.

A Venn diagram may help you with this task.

e.g., Find the HCF of
24 and 36
24 = 2x2x2x3 and 36 = 2x2x3x3
so the HCF of 24 and 36 is 2x2x3 = 12

The lowest common multiple (LCM), or least common multiple, is the smallest number that both numbers divide into exactly.

You can Find the LCM of
numbers by listing the prime factors of both numbers and then multiply all the prime factors of the larger number by those prime factors of the smaller number that are not already included.

e.g., Find the LCM of
24 and 36
24 = 2x2x2x3 and 36 = 2x2x3x3
so the LCM of 24 and 36 is 2x2x3x3 x 2 = 72

 

The Euclidean Algorithm

Connecting HCF and LCM

When you have found the HCF of the numbers a and b the LCM can be found using the following formula:

LCM = ab ÷ HCF

 

LCM Tutorial

HCF Tutorial

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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