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LCM. An easy method to work out the lowest common multiple in your maths exams.

Updated on May 04, 2011

The lowest common multiple of two or more numbers is the smallest number that is common to the multiples of the two or more numbers. The lowest common multiple is usually referred to as the LCM.

If you are trying to find the lowest common multiple all you need to do is write down the multiples of each of your numbers. Begin by writing down the first 5 multiples of each number, and continue adding more multiples if necessary until you come across the same multiple in each of your lists. This will be the LCM of your numbers.

Let’s take a look at some example on working out the LCM.

Example 1

Work out the lowest common multiple of 2 and 5.

First write down the first 5 multiples of 2 and 5.

The multiples of 2 are 2,4,6,8,10...

The multiples of 5 are 5,10,15,20,25...

As you can see the first multiple that you come across common to both lists is 10.

Example 2

Work out the lowest common multiple of 21 and 9.

First write down the first 5 multiples of 2 and 5.

The multiples of 2 are 2,4,6,8,10...

The multiples of 5 are 5,10,15,20,25...

As you can see the first multiple that you come across common to both lists is 10.

First write down the first 5 multiples of 21 and 9.

The multiples of 2 are 21,42,63,84,105...

The multiples of 5 are 9,18,27,36,45...

As you can see there is no multiple common to 21 and 9 in the first 5 multiples, so you need to write down some more multiples. Lets write down the next 5 multiples of each number.

21,42,63,84,105...,126,147,168,189,210...

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

As you can see the LCM is 63 as this is the lowest multiple common to both times-tables.

Example 3

Find the lowest common multiple of 20,25 and 40.

This time let’s write down the first 10 multiples of each number.

20,40,60,80,100,120,140,160,180,200...

25,50,75,100,125,150,175,200,225,250...

40,80,120,160,200,240,280,320,360,400...

200 is in all of the 3 lists so 200 is the LCM of 20,25 and 400.

Make sure that you don’t mix up the LCM with the Highest Common Factor (also known as Greatest Common Divisor).

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  • CyclingFitness profile image

    Liam Hallam 5 years ago from Nottingham UK

    Nice hub chap. Makes it all seem so straightforward. I used to love maths at school and when it's simplified and explained correctly it makes a whole world of difference.

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    Phillip Drayer Duncan 5 years ago from The Ozarks

    uggg I always hated math, but that was mostly because I had teachers that tended to go to fast without taking the time to dumb things down in to simple terms as you have here. Great job of explaining and making things simple to understand!

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