HCF and LCM – why?

Here’s another thing that is long past its expiry date.

What are Highest Common Factor and Least Common Multiple actually for? And “It makes adding fractions simpler” is just nonsense.  It may be that much later on, for those with a real interest in pursuing math, there is something useful there, but such people at that stage would be able to pick up the ideas and apply them in about 10 minutes.

If I want to add two fractions with different denominators then the simple and fairly obvious rule: “multiply top and bottom of each fraction by the denominator of the other one” is perfectly adequate, and if the student spots a common factor in the resulting fraction it can be removed then.

A separate but equally pointless activity is adding fractions with seriously different denominators. If you really want the answer then use a calculator. And get a clue about checking the result for realism.

I am sure there is more stuff in math courses which could be sent on its way, leaving time to do some interesting stuff.



Filed under arithmetic, fractions, Uncategorized

2 responses to “HCF and LCM – why?

  1. There is a recent tendency to tie exercises and activities in elementary math education to practical and immediate needs. Unfortunately, what is lost in these practical interpretations is the mathematical mental development inherent in those activities. HCF and LCM serve the purpose of developing a better visceral sense of multiplication and factorization, as do activities like finding the square root (manually) help build a better visceral sense of decimal fractions and real numbers.

    There was never a practical need for these activities, even 100 years ago. You don’t really believe that people without calculators went through the trouble of finding the GCM to add two fractions.

    There was and still is the same pedagogical and developmental need.

    Bob Hansen

    • OK, I’ll buy that, so long as something interesting is illuminated. For adding fractions (who does this?) we should keep things simple, and do the (ad+bc)/(bd) method, of course with natural development and full understanding. This is actually one of the cases where it is reasonable to go for understanding, but cruel to expect an explanation.

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