Maths help - LCM

[niadainud]

Please could someone tell me how to approach this question?

The Lowest Common Multiple of x and 180 is 360. Find the smallest possible value of x.

Thank you.

I can't I'm afraid as MathsWatch won't let you reopen the question once it's submitted. But @SeptemberIRememberALoveOnceNewHasNowGrownOld has solved it.

See photo.

Thanks. What confused me before was the 3 suddenly disappearing from the answer, but then I realised that that indicated 3k and you were asked to find k.

Could you possibly set me a similar question to practise on?

I can’t see why they give you a mark for 24.

With LCM the answer can't just be 2 as 180=2x90
Similarly 180=4x45

But 8 doesn't divide into 180 (8×22.5) but does into 360 (8x45)

Similar question, without writing out all the words but same method. Find k.

No, me neither. Nor 360! Maybe it's a glitch?

24 would give the correct LCM but is not the smallest possible number. Similarly 360.

How can it be the lowest but not the smallest?

Almost missed that! Thank you very much.

Because any multiple of 8 would also not have 180 in its time table, so would share 360 as the lowest number in common. But once you realise what times tables include 360 (36 for ease of thinking) you can work out the smallest number which doesn't have 18 in the times table but does have 36- which gives you 8.

The LCM =360 is the lowest number divisible by 180 and the unknown number.
The unknown could be 8, or 24, or 40 or various other options
They want you to find the smallest of the possible options, ie 8.
However they have decided to give you a mark for any answer that gives an LCM of 360.

@Barleysugar86 Not any multiple of 8. Eg 56=7x8 but wouldn't give LCM=360 as 7 is not a factor of 360.

The LCM of 2 and 180 is surely 180? Which is why it wouldn’t score. 24 and 360 are right.

Sorry missed the find the lowest possible x … 8 would be the lowest I think.

I get k = 10x + 3. Is that right?

😀

(Sorry for slow replies now. I’m eating.)

Excellent! It makes much more sense now. Thanks for coming up with the practice question.

Lowest common multiple means - if you write out all the multiples, find the first one that both numbers have in common.

It isnt 2, because 180 is a multiple of 2. It isnt 4 either for the same reason.

If you are not clear what LCM means, go back to the method where you write out every multiple. Once you are confident you can move on to the venn diagram method which is a shortcut

Back to the original question:
I have just consulted my very-good-at-Maths DH.
He said 360 at first. When I asked him why 24 also got the mark, he thought a bit and said that the answer is 24, not 360.

Sorry for misleading you.

Hmm. The only answer that gets full marks is 8...

It is 8 😀

I’ll find my coloured pens and write out a solution.

8 gets full marks because it is fully correct.

24 and 360 give an LCM of 360, so 1 mark for partial correctness, but neither are the smallest possible which is what was requested, so don't gain full marks.

It's just clicked. I am x to the power doofus and my lowest common multiple is muppet.

See photo first:

Thinking about 180, you need an extra 2 to get 360.
You’ll need the two 2s you already have as you need to see three of them in x (the number you’re trying to find) so the answer is 2 x 2 x 2 = 8.

I agree with @TeenToTwenties last comment. I hadn’t realised that 8 was a 2 mark answer. I thought 24 and 360 were the only answers which gave any marks.

What this shows, in my opinion, is that it was a hard question!

Are you used to using Venn diagrams to answer questions on HCF and LCM, @niadainud? If, like me, diagrams can help you to solve Maths problems then I think it’s a good technique to learn.

Thanks very much @SeptemberIRememberALoveOnceNewHasNowGrownOld .

I clearly need to practise my HCF and LCM.