At least in my country, the explanation of the basic operations over rational numbers is done very near to the concept of primer number, prime factorization and calculus of least common multiple. In fact, usually l.c.m is explained previous to fractions.
This is a real and typical example of text:
"Addition and subtraction of fractions with same denominator: add or subtract the numerators and keep the denominators [... some examples ...]. To add or subtract fractions of different denominator: convert all fractions to common denominator, obtain the l.c.m. of all denominators [...]"
You can see in previous text how the concept of common denominator is put so near to the one of l.c.m that easily one of them replaces the other. The drawback of this approach is that students loss the basic concept of the operations in a mix of concepts and a nightmare of l.c.m algorithm.
My question is:
- is it done in this way in most of other countries ?
- advantages and disadvantages of discard the concept and mechanics of l.c.m until more advanced learning stages.