At least in my country, the explanation of the basic operations over rational numbers is done very near to the concept of prime numbers, prime factorization, and the calculation of the 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 their common denominator, by obtaining the l.c.m. of all denominators [...]".
You can see in the previous text how the concept of common denominator is based on the concept of l.c.m., that easily one of them replaces the other. The drawback of this approach is that students lose the basic concept of the operations in a mix of concepts and a nightmare of l.c.m algorithm.
My questions are:
- Is it done in this way in most other countries ?
- What are the advantages and disadvantages of discarding the concept and mechanics of l.c.m. until more advanced learning stages?