I read in this school book, an algorithm to find the LCM of rationals. It goes in the following manner. $[\frac{a}{b}, \frac{c}{d}]=\frac{[a,c]}{(b,d)}$.
If you inspect as to why the formula is given so you will realise that this formula gives the smallest positive rational which is an integral multiple of both $\frac{a}{b}$ and $\frac{c}{d}$.
For example, $[\frac{1}{2}, \frac{3}{4}]=\frac{3}{2}$. Where, $\frac{3}{2}=3(\frac{1}{2})=2(\frac{3}{4})$.
Now, what is puzzling me is the idea of LCM. Because I was of the opinion that this is a concept only defined on integer, but here they define it for rational numbers. So, is this a universally accepted formula or was it just something the person who wrote this book put in?
I just realised that someone has already asked a question previously questioning the logic behind this formula. Well, that is not my question. I wish to know whether this formula is actually relevant in higher mathematics.
