LCM of irrational numbers So i read in a book that irrational and rational numbers do not have a common multiple and it said that lcm of irrational numbers is also only possible when both the irrational numbers have the same surd. I was wondering what this means.

https://www.quora.com/Does-the-L-C-M-of-two-irrational-numbers-exist
With $5*\sqrt{2}$ and $3*\sqrt{2}$ their least common multiple is $15*\sqrt{2}$, because it's the smallest number that's an integer multiple of both.
However, they don't always have an LCM. Take $\sqrt{2}$ and $\sqrt{3}$. There is no number $L$ such that $\frac {L}{\sqrt{2}} $ and $\frac {L}{\sqrt{3}}$ are integers, otherwise their quotient, $\sqrt{\frac {2}{3}} $, would be rational. And it isn't.
