Lesson video

Hi, everyone.

I'm Mr. Lund.

And in this lesson, we're going to be finding the lowest common multiple of two numbers using Venn diagrams. Hi everyone.

Before finding the lowest common multiple, we're going to learn how to write a number as the product of its prime factors.

Let's start with the number 80.

If I find a factor of the number 80, let's say the number eight, then I can find it's factor pair.

There we go.

Now eight and 10 are not prime numbers.

So, let's continue this process of breaking our numbers down into factor pairs.

Eight has factor pairs of two and four.

Notice that one of those numbers is prime.

So let's circulate.

10 has factor pairs of two and five.

Both of those numbers are prime.

So let's circle those primes.

Four is not prime and can be broken down into the factor pairs of two and two.

Let's circle them.

If I were to start the whole process by dividing by a different number, let's divide 80 by five to find a factor pair of five and 16, then circle your prime number.

16 can be broken down into factor pairs of four and four.

The number four can be broken down into factor pairs of two and two.

Let's circle all our prime numbers.

And we can see that the product of prime factors is exactly the same.

80 is two multiplied by two, multiplied by two, multiplied by two, multiplied by five.

We can write that simplified in index form.

So how well did you understand that explanation? Here are some questions for you to try.

Pause the video and return to check your answers.

Here's the solution to question number one.

You could have also written 18 in terms of its prime factors, by starting off with two and nine, as your factor pairs.

You still get the same product of prime factors, two times by three squared.

There we go.

Here is our question two.

Everybody likes our lovely number two.

Let's pause the video and check your answers when you return.

Here's the solutions to question number two.

Here is my example of a factor tree of a hundred.

I've decided to start with the number 25, because I know that it is five squared and four is two squared.

So that gives me my answer there.

Check, check your answer, multiply them together at the end, just to check that you come back to the start.

Now we can use the lowest common multiple of two numbers using their prime factors.

Here's the number 80 and the number 45 broken down into its prime factors.

Let's use this Venn diagram and start our process by looking for any common prime factors.

In this case, the only common prime factors between our two numbers is the number five.

Let's cross them off our factor trees, placing the remainding prime factors into the correct parts of the Venn diagram, remembering to cross off each element from the factor trees as they are inputted into the diagram, finds us this as a result.

The lowest common multiple can then be calculated by multiplying all the elements within our Venn diagram.

That finds the lowest common multiple to be equal, to be 720.

The lowest common multiple of 80 and 45, is 720.

How well did you understand that? Pause the video and return to check your answers.

Here's the solution to question number three.

Some of you may have made the mistake of putting two twos in the intersection.

Remember if they are common, the intersection just needs a one, two.

If you can work these out without having to work out the prime factors and use Venn diagrams, that's totally fine, but get a little bit of practise with that technique.

It might be helpful in the future for you.

Pause the video and return to check your answers.

Here's the solutions to the final questions.

You don't have to use Venn diagrams. You could use listing as well, but using Venn diagrams means that if you ever get a question like that in your exam, you can answer it for starters, and equally, if numbers are really big, Venn diagrams and the prime factor decomposition, as they say, really comes into its own, okay? Unless you're using a computer of course and then you just bung it in, anyway.