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.

180 is a factor of 360. So the LCM is 360.
(LCM - smallest number which both divide into without a remainder)

2 x 180 is 360. X is 2

Gosh, is it really that simple?!

Ok, what about: Write 180 as a product of its prime factors?

I've got 2 x 2 x 3 x 3 x 5.

I thought it was 2, but I'm doing this on MathsWatch and if I put in 2 I don't get any marks. If I put in either 24 or 360 I get a mark. Makes no sense...

And also: 27 x 9 3x can be written in the form 3k Find out what k is an expression in term of x.

Thanks.

Edit: It's supposed to be 27 x 9 to the power 3x can be written in the form 3 to the power k.

Huh, ok I will think again.

180=10×18=2×5×2×3×3
You need an extra ×2 to get 360
Therefore the smallest value of the other number is 2x2x2=8

(Ps I am confident I am right, maths degree and have helped DDs in recent years to GCSEs)

To write a number as the product of its prime factors there are several methods but I’ll go with this one as it’s the easiest to type on a phone:
Divide by the smallest prime number, which is 2.
Keep on dividing by 2 until it won’t divide exactly.
Then do the same by dividing the next by the next smallest prime number, which is 3.
Then the same with 5, 7, 11 etc until the answer is a prime number.

So
360/2 = 180 (that 2 will be part of your answer)
180/2 = 90 (2)
90/2 = 45. (2)
45/3 = 15 (3)
15/3 = 5 (3)
5 is a prime number
So, using the numbers in brackets, 360 = 2 x 2 x 2 x 3 x 3 x 5.

8,
180 = 2x2x3x3x5
360 = 2x180
hence want to have a value with an extra 2, lowest value would be 2x2x2 = 8

If I have understood your second question

Your answer at 19:15 - if you multiply those numbers together you get 180, so you need to add another x2 .

Edit - sorry, I misread. You wanted 180 not 360, so your answer is right.

Thank you. Please could you explain:

a) Why you wrote 2 x 5 x 2 x 3 x 3 instead of 2 x 2 x 3 x 3 x 5? I realise that multiplication is commutative, but was there a reason for the order you chose?

b) Why the smallest value of the other number is 8? I see you're combining factors, but how do you know which ones to use?

Yes, you are right!

Lcm is like the union of 2 sets

Apparently the answer is k = 3 + 6x. But I can only just about follow the working out; I don't think I'd get there on my own.

Thanks. The overlapping part has 2 squared not cubed, so why is the answer 8, not 4?

It is indeed easier to hand write and photograph 😀

Edit - click the photo to see the whole solution

I think I get it! You have cancelled out the two 3s as that would give you 3k, so you're left with 1k (i.e. k) = 6x + 3. Is that right?

Yes, I think photographing is the way forward...

The intersection of the prime factorisation gives the HCF.
You are trying to find the total number in the RH circle. You need another 2 over and above the 2x2 you already have.
They must be shared otherwise you haven't drawn the intersection right.

If you let us know what level of Maths you have achieved already and are aiming for we can give explanations at the appropriate level. 😀

Can you photo the second question, I didn't understand there are actual x's in the question, I thought they were multiplication signs.

Yes, sort of. It’s called equating the powers (or exponents.)

Sort of! Yes, I realise my grasp is a bit shaky at the moment...

I did GCSE about a hundred years ago and got a C. I'm now redoing it for fun and trying to properly understand the concepts and processes of the more advanced stuff, so hoping to get a higher mark this time round.