# Lesson video

In progress...

Oh, hi everyone.

In this lesson, we're going to be playing the lowest common multiple and the highest common factor in problem solving star questions.

Hi everyone.

Trains from Leeds to Manchester depart the station every 12 minutes.

There's one now.

Trains from Leeds to London depart the station every 16 minutes.

Off we go.

A Manchester and a London train both depart at 9:00 a.

m.

At what time will the Manchester train and the London train depart the station at the same time? Let's use our knowledge of lowest common multiples to help us answer this question.

If trains are leaving from Leeds to Manchester every 12 minutes, I can write out the multiples of 12 like so.

If trains from Leeds to London depart every 16 minutes, let's write the multiples of 16.

Finding the lowest common multiple will tell us that after 48 minutes, trains will depart at the same time.

So, the next time that both these trains will depart will be at 9:48 a.

m.

Here are some more problem solving questions involving your understanding of the lowest common multiple.

Here are the solutions to question number one.

You could have used listing.

Here I've listed the multiples of 15 and 18.

There we go.

Finding the lowest common multiple of 90.

A lovely number two for you.

Here's the solution to question number two.

Hopefully, you can start to see that the lowest common multiple has quite a significance when we're thinking about synchronising time.

Where else would you see synchronisation of time? In music of course.

One, two, three, four, five, six, seven, eight.

One, two, three, four.

Here you are given two numbers, A and B written in prime factorised form.

Use a calculator to find the value of A.

A is equal to 5,250.

To calculate the lowest common multiple, you can use a Venn diagram.

Look for any prime numbers that are common to both A and B and place them in the intersection.

Completing the Venn diagram, you then multiply all the elements together to find a solution of 10,500.

If I want to find the highest common factor of these two numbers, I simply look in the intersection of the Venn diagram and multiply all these numbers together.

That finds me that the highest common factor is equal to 30.

Finally, does B equally divide by 15? Yes, it does.

Because three and five are factors.

Three times by five equals 15.

Here are some questions for you to try.

Here's the solutions to question three.

I've taken the time to create my own Venn diagram.

And I like this question.

I mean, if you can get your head around it, what a wonderful thing to be able to do to be able to work out the lowest common multiple of 3,150 and 163, sorry, 168, just by this technique.

I do like it.

Well done for getting this far.