Lesson video

Hi, I'm Miss Kidd-Rossiter and I'm going to be taking the lesson today on the LCM and prime factors.

It's going to build on the work that you've already done on lowest common multiple highest common factor and prime factorization.

So hopefully you're really going to enjoy it.

Before we get started you're going to need a pen and something to write on so make sure you've got that.

Try and get yourself into a nice, quiet place, free from all distractions.

If you need to pause the video now to sort anything out, then do, if not, let's get going.

So today's try this activity, you've got to find the first five common multiples of 12 and nine.

There's a diagram on the board, a representation that might help you.

And then I'd like you to write each as a product of their prime factors.

When you've done that, can you notice anything interesting about the five common multiples? Pause the video now and have a go at this task.

Excellent work, let's go through these then.

So your first five common multiples are 36, 72, 108, 144 and 180.

We can know once we found the first common multiple, that any other common multiples will be a multiple of the first common multiple.

When we've got 36, where in here can I see nine? And where can I see 12? Pause the video now and think about that.

Excellent, I can see nine here can tie in three times three.

And I can see 12 here as two times two times three.

Can you see them in the other common multiples? Excellent, and they're in all of them, aren't they? So here they are in 72, here they are in 108, here they are in 144 and here they are in 180.

Now what's different about 36 compared to the other four common multiples? Pause the video and think about that.

Excellent, 36 uses the minimum number of prime factors, doesn't it? It exploits the overlapping primes, which in this case is just the three and adds no extras.

Now it makes sense here because we've got to multiply our 36 by two to get 72, to get 108 we multiply our 36 by three, and to get 144 we multiply our 36 by four, and to get 180, we multiply our 36 by five.

So we're going to have a little bit more of a look at this now.

So before we do pause the video, and explain how each strategy can help you find the lowest common multiple.

So pause now.

Excellent, let's look at these two strategies first.

Well, these are basically the same strategy, aren't they? They're both listing strategies.

So here we just list the multiples of 18, and here we list the multiples of 15, and then we find the lowest common multiple.

So the first multiple that is common to both.

This is just a representation of that structure where we use a length to represent 15 and 18.

And we see that six 15s are the same as five 18s.

So we would know that this is 90.

And this is 90, so therefore the lowest common multiple must be 90.

This is slightly different.

So what we've done here is we've made use of everything that we know about prime factors.

So 18 as a product of its prime factors is what? Tell me now.

Excellent, two multiplied by three multiplied by three.

And 15 as a product of its prime factors, this is what? Excellent, just three multiplied by five.

So how could I get my lowest common multiple from here? So you can see that I've organised my prime factors into a Venn diagram.

The common prime factor to 18 and 15 is three.

So I've put three in the centre of my Venn diagram.

Then any that I have leftover two and three for 18, go in this circle and five for 15 goes in this circle.

So if I was to do two times three times three times five, I would get my lowest common multiple, which is 90.

Why does that work? Pause now and think about it.

Excellent, if I multiply the two times three times three, which is my 18 by five, then it ensures that 15 is a factor, and if I multiply my three by five by six, then that ensures that 18 is a factor, which you can see more clearly here.

So you're now going to have a go applying your learning to the independent task.

So pause the video now navigate to the independent task.

And when you're ready to go through some answers, resume the video, good luck.

Excellent, let's go through some of these answers then.

So you have these four Venn diagrams, where they are completed and you've got your lowest common multiple written next to them.

If you need to pause the video now to look at these answers, then please do.

Excellent, and then for these ones, you've got the answers on the screen there as well, excellent work.

Finally then moving on to the explore task, the prime factors of two numbers in the Venn diagram, can you find what the two numbers are, any common factors, their lowest common multiple, and their highest common factor.

Pause the video now and have a go at this task.

Excellent work, so let's first of all, work out what this circle on the left is representing.

So we can see that the prime factors of this number are two, two, five and five.

So that means if we multiply these together, two times two is four, four times five is 20, 20 times five is a hundred that means that this number represented by the left hand circle must be a hundred.

Similarly for the one on the right hand side, we know that the prime factors are two, two, three, five, and seven.

And when we multiply these together, five times seven is 35, 35 multiplied by three is 105, multiplied by two is 210, multiplied by two again is 420.

So that must be the number represented on the right hand side here.

Now you noticed I worked backwards there, and it doesn't matter which way you do the multiplication 'cause you know, from all your work so far, that multiplication is commutative.

And I found that easier because I know that if I get a big number here, I find it easier to double it and then double it again at the end.

Any common factors then, will all numbers, all positive integers, have a common factor of what? Excellent one, so one has to be a common factor.

What else is a common factor? Two is a common factor.

Is three a common factor? No, it's not because if it was, it would be written here in the centre, wouldn't it? It's a prime factor.

Is for a common factor? Yes it is because we can get it from multiplying two and two.

Is five a common factor? Yes it is and we can keep going like this, all your common factors they're there on the screen.

So one, two, four, five, 10, and 20.

The lowest common multiple then so to work this one out, remember we have to multiply two, two, three, five, five, and seven, and we get an answer of 2,100.

And the highest common factor to them, what do you think the highest common factor is? Did you manage to figure this out? So the highest common factor we get from the centre of the Venn diagram, so that gives us two multiplied by two, multiplied by five, which is 20.

That's the end of today's lesson.

So thank you very much for all your hard work.

I hope you've enjoyed the lesson.

Don't forget to get go and take the end of lesson quiz so that you can show me what you've learned and hopefully I'll see you again for another math lesson soon, bye.