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Hello and welcome to another video.

In this lesson, we'll be looking at common multiples.

Again, my name is Mr. Maseko.

Make sure you have a pen or a pencil and something to write on.

Okay, now that you have those things, let's get on with today's lesson.

Try this activity, make sure you read each statement carefully.

So pause the video here and give this a go.

Okay, now that you've given this a go, let's see what you've come up with.

Well, for a multiple of 11, we're looking for any number in the 11 times tables.

So you could have had 11, 22, 33, or even 44.

So any number in the 11 times table.

For a factor of 100 and a multiple 5.

Well, multiples of five are the numbers in the five times table, so if we look at the numbers of the five times table, let's say 5, 10, 15, 20, 25, and so on, which of those are factors of 100? Well, five is a factor of 100 because 5 times 20 gives you 100, which also means 20 is a factor of 100.

You can also have 10 as a factor of 100, also 25 as a factor of 100.

You could have also had 50, that's also a factor of 100 and a multiple of 5.

A multiple of a square number.

Well, what are the square numbers? 1, 4, 9, 16, 25, 36.

And you want a multiple of a square number, really you could have had any number at all because every number is a multiple of one.

And then a multiple of both four and three, well, you could have had 12 because 4 times 3 gives you 12, and 3 times 4 gives you 12.

You could have at 24, 36, etcetera, etcetera.

Now, if we're looking at this, were talking about common multiples, and we can represent this using a bar model and any time the bars align, there's a common multiple.

So if you look 3 times 4, that gives you 12.

So you can see four 3s, that makes 12, and three 4s makes 12, so 12 is a common multiple.

And then there's also another one here, and that's a 24, we've already seen this.

So every time you have three 4s or every time you have four 3s, you have a common multiple.

Now 12, the first common multiple between 3 and 4, this has a special name.

Do you know what it is? Well, it's very obvious, this is the lowest common multiple.

It's the lowest and it's a common multiple.

See, nice easy name to remember.

Now, if you look at six and nine, we know that 36 is a common multiple of 9 and 6.

Well, how do we know? We know that 9 times 4 gives us 36, and 6 times 6 gives us 36.

You draw a bar model to show that answer is correct.

Pause the video here and give this a go.

Okay, now that you've tried this, let's see what you've come up with.

Well, you should have come up with something that looks like this, and you notice a 36 after six 6s there, that is 36.

But see, 36 is not the first common multiple between nine and six.

What is the first common multiple? Remember we call the first common multiple, the lowest common multiple.

This right here, there after three 6s or two 9s, at the lowest common multiple, call that the lowest common multiple.

LCM, Lowest Common Multiple, and that would be 18.

That is the first number that appears in the six times table and also in the nine times table.

For this independent task, I want you to sort the integers from 1 to 40 in the Venn diagram, and then answer the questions after that.

Now if you'd like a clue, continue watching the video, but if you want to get on with this straight away, pause the video in 3, 2, 1.

Okay, for those of you that want a clue, let's think of the number one.

Is the number one a multiple of six? Well, no it isn't.

How about is it a multiple of four? No.

Is it a multiple of five? No.

So then number one would be outside.

What about, let's take the number 12.

Is the number 12 a multiple of 6.

Yes.

So we're looking at the number 12, is the number 12 a multiple of 4? Yes.

Is it a multiple of 5? No.

So it's a multiple of six and four, so that would go here, but since it's not a multiple of five, it can't go in the middle.

Okay, now that's your clue, so pause the video and continue this task.

Hello everyone, my name is Mrs. Jones, and I'm going to be taking you through the solution to this one, or these four questions.

So question one asks you to sort out numbers 1 to 40 into this Venn diagram.

So we already did 1 and 12, so let's just go through them.

Two, okay, two isn't a multiple of four, six, or five, it's fewer than all of them, so it would definitely be less than the first multiple of each of those.

Three is also outside of the Venn diagram.

Four is the first one in the Venn diagram and it's multiple of four, the first multiple of four.

Five will be the first multiple of five, so it's in there.

And six, the first multiple of six.

Seven would be outside of the Venn diagram, it's not a multiple of any of them.

Eight is the second multiple of four, should be in there, but it's not a multiple of six or five.

Nine would be outside of the Venn diagram.

10 is a multiple of 5, so it should be in there, and it's not a multiple of any of the others.

11 would be outside of the Venn diagram.

12 we've already put, so it's in there, and 13 is outside of the Venn diagram, 14 outside of the Venn diagram as well.

15 though, is a multiple of five.

16 is a multiple of 4.

17 outside of the Venn diagram.

18 multiple of 6.

19 is outside of the Venn diagram.

Where would 20 be? 20 is a multiple 4 and it's also a multiple of 5, so it should be there.

21 is outside the Venn diagram.

22 is outside the Venn diagram.

23 is also outside.

And 24 is a multiple 4 and 6, so it should be just in between four and 6 there.

25 is a multiple of 5.

26 is outside the Venn diagram.

27 is outside the Venn diagram.

28 is a multiple of 4, so it should be in that right circle.

29 is outside the Venn diagram.

30 is a multiple of 6 and 5, so we've got it just there in between 6 and 5.

31 is outside the Venn diagram.

32 is a multiple of 4, so it's just there.

33 is outside the Venn diagram.

34 is outside the Venn diagram.

35 is a multiple of 5, so it should be in that circle only.

36 is a multiple of 6 and 4, so it should be in that top box there between 4 and 6.

37 is outside, 38 is outside, 39 is also outside, and 40 is a multiple of 4 and 5, so it should be just there.

Okay, so that's question one.

Make sure, you know, you pause and double check yours if you've got any, perhaps that you might have miss out or put slightly differently, you have a think about why? Moving on to question two, in which section would you find multiples of 20? Interesting.

Well, we can see them quite clearly now that we've sorted these out, we've got both 20 and 40 in this section here.

If we had further multiples 20, think about where they would go.

But yeah, this to be a great place to start looking a multiple of 20, because 20 itself is a multiple of 4 and 5, it's multiples will also be a multiple of four and five.

Interesting that we've got nothing in this middle section.

I wonder if any multiples of 20 would also appear as a multiple of six as well? Something to think about.

Question three, where would you find prime numbers? Okay, well we know what prime numbers are.

Prime numbers only divide by themselves and one.

So it wouldn't necessarily be a multiple of these, however, there is one prime number within our Venn diagram, and that's the number five, the first multiple of five only divides by five and itself, okay? Anything in here are also, if we look at four, it's also a multiple of two, six is also a multiple of two.

So even the lowest multiples in here can not be prime numbers.

All the other prime numbers would be on the outside of the Venn diagram, but it doesn't necessarily mean that all of these are prime numbers, some of them might be multiples of three, for example, or multiples of other numbers.

So you'd have to still think about which ones were prime numbers carefully.

What is the lowest common multiple of six and four? Okay, so I'll need to look in this section, because I know that my number has to be a multiple six and four.

So it looks like the lowest one here is 12.

Okay, I'm going to pass you back over to your teacher to finish the lesson.

Now here's an explore task for you to try.

Two students have two contradicting statements, pause the video here and give this a go if you don't want to clue.

Now, if you want a clue, keep watching.

Okay, for those of you that want a clue.

Well, one student says some groups of integers will have no common multiples.

Another one says you will always be able to find a common multiple.

Who do you agree with and why? So, what I want you to do is just pick two numbers.

So let's say the numbers six and seven, and see if you can find a common multiple just by listing the multiples.

So 6, 12, 18, 24, etcetera, etcetera.

Then 7, 14, 21, and then 28, you keep going.

What you find is that both of them have 42 in their times table, and that's a common multiple.

Now see if you can find a number that you can't find a common multiple for.

So now pause the video here and give this a go.

Okay, so now that you've tried this, let's see what you've come up with.

Well, if we think about it, so one students says some groups will have no common multiples.

Could that be true? Well, this cannot be true because like when we have six or seven, if we're struggling to find a common multiple, you could have just done six multiplied by seven, which gives us 42.

So when we multiply the two numbers together, we'll always find a common multiple.

So you can pick any numbers you want.

So if you have, let's say, 10 and 13, well, if you want to find a common multiple, what can you do? Well, you can just do 10 multiplied by 13, which is 130.

So for any group of numbers, you can always find a common multiple, because you can just multiply the numbers together and you will find a common multiple.

Okay, now I really do hope that you've enjoyed this lesson.

If you want to share some of the work that you've done, ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you for participating in today's lesson.

Bye for now.