- #1

chwala

Gold Member

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- 354

- Homework Statement
- see attached

- Relevant Equations
- Ring Theory

My interest is on the highlighted part ...

Now to my question,

in what cases do we have ##mn<(m,n)[m,n]?##

I was able to use my example say,

Let ##m=24## and ##n=30## for example, then

##[m,n]=120## and ##(m,n)=6## in this case we can verify that,

##720=6⋅120## implying that, ##mn≤ (m,n)[m,n]##.

Now to my question,

in what cases do we have ##mn<(m,n)[m,n]?##

I was able to use my example say,

Let ##m=24## and ##n=30## for example, then

##[m,n]=120## and ##(m,n)=6## in this case we can verify that,

##720=6⋅120## implying that, ##mn≤ (m,n)[m,n]##.