Help with simple equation

I was struggling with this equation...

1/3n + 1/4n = 7/24

I've now realised I had to add the first two terms to get 7/12n, but I was originally trying to multiply the entire equation by the LCM which was 24, which resulted in 8n + 6n = 7...

... so why doesn't that work? For example with something like 2/a = 3/8 you would multiply the equation by the 8a, but that doesn't work for my previous example

Thanks for any help

Multiply both sides by 24n:

24n/3n + 24n/4n = (7 * 24n)/24

8 + 6 = 7n

14 = 7n

n = 2