# 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.

##### SieveTreesLevel 1Level 2Level 3Level 4Level 5DescriptionHelpFactorsMultiples

This is level 2; Finding the lowest common multiple (LCM) of two numbers You can earn a trophy if you get at least 9 correct and you do this activity online.

 Find the LCM of6 and 9. Find the LCM of2 and 4. Find the LCM of4 and 5. Find the LCM of6 and 18. Find the LCM of35 and 21. Find the LCM of36 and 27. Find the LCM of24 and 60. Find the LCM of56 and 40. Find the LCM of28 and 21. Find the LCM of136 and 51. Find the LCM of20 and 27. Find the LCM of52 and 65.
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This is HCF and LCM level 2. You can also try:
Level 1 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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Interactive number-based logic puzzles similar to those featuring in daily newspapers designed to develop numeracy skills. These puzzles are drag and drop and can earn you a Transum Trophy.

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## Teachers

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/software/SW/Starter_of_the_day/Students/HCF_LCM.asp?Level=2

## 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.

## 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.

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

## 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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