Least common multiple

[darkyadoo]

Hi,

The LCM of two numbers is 18. One of the numbers is 18.

1. Write down all the possibilities for the other number.
2. Describe the set of numbers you have created.

The set I propose is $\big\{1,2,3,6,9,18\big\}$

The correction doesn't include 18 ...? Should I include 18?

Thanks

 

[darkyadoo]

I add another information, we can consider the LCM as a function such that :$$\begin{array}{ll}LCM:&\N\times \N\to \N\\&(x,y)\mapsto LCM(x,y)\end{array}$$, thus, we are looking for $x\in \N$ such that $$LCM(x,18)=18$$, that is why I propose the set $\big\{1,2,3,6,9,18\big\}$

 

[lev888]

Hi,


The set I propose is $\big\{1,2,3,6,9,18\big\}$

The correction doesn't include 18 ...? Should I include 18?

Thanks

By proposing you mean guessing? There is no guessing in math. Please post your solution.

 

[darkyadoo]

Thank you sir! I have a French degree in math with honour, and I want to teach in UK so I must take the GSCE in math or an equivalent, furthermore we all know that maths from 13 to 16 years old are not rigourous !! So my solution is the one I have already proposed.

 

[lev888]

Thank you sir! I have a French degree in math with honour, and I want to teach in UK so I must take the GSCE in math or an equivalent, furthermore we all know that maths from 13 to 16 years old are not rigourous !! So my solution is the one I have already proposed.

By solution I mean the work that justifies the answer.

 

[darkyadoo]

too long, it takes 5 pages of calculations

 

[topsquark]

too long, it takes 5 pages of calculations

Well if you are looking for x such that LCM(x, 18) = 18 x can't be any bigger than 18 can it?

-Dan

 

[darkyadoo]

$$LCM(x,y)=18\iff\Big\{(x,y)\in \N^2 :(x\mid 18\,\text{and}\,y\mid 18)(\forall n\in [\![0,17]\!]:(x\nmid n\,\text{and}\,y\nmid n))\Big\}\underbrace{\iff}_{y:=18}\big\{x\in \N:x\mid 18\big\}=\big\{1,2,3,6,9,18\big\}$$

 

[darkyadoo]

My problem is not to find the solution, but to know why the Edexcel GCSE maths book excludes 18 of the set of solutions

 

[darkyadoo]

 

[pka]

Because $LCM\{1,18\}=18$.

 

[darkyadoo]

I don't understand, this proposition is true: $\forall n\in \{1,2,3,6,9,18\} :LCM(n,18)=18$

 

[JeffM]

This is purely a linguistic issue.

The set of integers of which 18 is the least common multiple is indeed 1, 2 , 3, 6, 9, and 18.

One of the numbers is 18. What are the other numbers. It is a question about the meaning of the word "other."

 

[darkyadoo]

ok,thank you but the question is Write down all the possibilities for the other number.

we are talking about "the other number" in singular, and not "the other numbers", anyway I wanted to be sure that was typo. I was thinking that it may be another definition for the least common multiple given at the level.

Thank you very much everyone for your help!

 

[JeffM]

we are talking about "the other number" in singular, and not "the other numbers", anyway I wanted to be sure that was typo. I was thinking that it may be another definition for the least common multiple given at the level.

Thank you very much everyone for your help!

"All the possibilities for the other number" excludes 18, but includes 5 other numbers. It is a test of your ability to construe English.

 

[darkyadoo]

"All the possibilities for the other number" excludes 18, but includes 5 other numbers. It is a test of your ability to construe English.

Sorry but I am French so maybe there is something I missed.

The LCM of two numbers is 18. One of the numbers is 18. (nothing says that this two numbers are distinct)

That means: Given two numbers $x,y$ such that $LCM(x,y)=18$ and $y:=18$


Write down all the possibilities for the other number. (we are speaking about x, so nothing excludes that x could be equal to 18)

What do you think ?

 

[JeffM]

I actually know something about explaining English.

User Jeff Morrow

Q&A for speakers of other languages learning English

ell.stackexchange.com

Perhaps in French "l'un" and "l'autre" may refer to the same thing, but in English "one" and "the other" refer to distinct things.

Is the question as clear as possible? No. But the normal, everyday meaning of the question is "What are the numbers whose lowest common multiple is 18 OTHER than 18 itself?" And quite obviously, the answer is 1, 2, 3, 6, and 9.

This whole thread is about interpreting ordinary English prose, not mathematics or the definition of least common multiple.

 

[darkyadoo]

I actually know something about explaining English.

User Jeff Morrow

Q&A for speakers of other languages learning English

ell.stackexchange.com

Perhaps in French "l'un" and "l'autre" may refer to the same thing, but in English "one" and "the other" refer to distinct things.

Is the question as clear as possible? No. But the normal, everyday meaning of the question is "What are the numbers whose lowest common multiple is 18 OTHER than 18 itself?" And quite obviously, the answer is 1, 2, 3, 6, and 9.

This whole thread is about interpreting ordinary English prose, not mathematics or the definition of least common multiple.

thank you for your answer

 

[lev888]

I actually know something about explaining English.

User Jeff Morrow

Q&A for speakers of other languages learning English

ell.stackexchange.com

Perhaps in French "l'un" and "l'autre" may refer to the same thing, but in English "one" and "the other" refer to distinct things.

Is the question as clear as possible? No. But the normal, everyday meaning of the question is "What are the numbers whose lowest common multiple is 18 OTHER than 18 itself?" And quite obviously, the answer is 1, 2, 3, 6, and 9.

This whole thread is about interpreting ordinary English prose, not mathematics or the definition of least common multiple.

I see the 2 numbers as 2 independent variables. One is 18. What are the possibilities for the other variable? Seems like 18 is one of the possibilities.

 

[JeffM]

I see the 2 numbers as 2 independent variables. One is 18. What are the possibilities for the other variable? Seems like 18 is one of the possibilities.

"One number is 18" That is not a variable at all, let alone an independent variable. What are "all the possibilities for the other number." That word "other" excludes 18. This is not math; this is what "other" means in English.