# LCM

## Finding the Number of Ordered Tuples Having a Given LCM

Counting is one of the first skills that a student of mathematics learns. Here we feature an article that observes patterns while counting and generalises this pattern. While the actual combinatorics and use of the binomial theorem may be appreciated only by students of classes 11 and 12, students of High School will certainly be able to follow the reasoning in the two examples given. It is important for students to have such gentle introductions to mathematical notation and theorems used at a more senior level.

## Extending the Definitions of GCD and LCM to Fractions

With the LCM and GCD of natural numbers well- defined and an integral part of the middle school curriculum, one may wonder why this article embarks on a rather theoretical study of the LCM and GCD of rational numbers. But this article depicts exactly what a mathematician does – take a well-known concept and extend it to larger sets, testing the extended definition with backward compatibility with the original set. For the more able middle-schooler, this is an excellent opportunity to flex the muscles of conceptual understanding and constructive reasoning.

## LCM Visualization And Fractions

This article explains the concept of LCM visually, and also helps students appreciate why LCM needs to be used when solving certain type of problems and puzzles.

## Middle School Mathematics some reflections

A. Ramachandran shares his reflections on the trials, travails & triumphs in middle school mathematics teaching.

## Activities and Questions Around Factorisation

Here is an interesting exercise in factorisation with boundary conditions, for students of upper primary school – classes 5, 6 and 7.

## AtRiA: Problems for the Middle School - July 2013

Here are some problems for the Middle School, edited by R. Athmaraman. The solutions to problems posed will appear in the next issue of AtRiA's problem corner. Also find the solutions to the problems given in AtRiA March 2013 Issue-II-1

## AtRiA Problems for the Middle School - March 2013

The problems in this selection are all woven around the theme of GCD (greatest common divisor, also known as, highest common factor) and LCM (least common multiple). The solutions to problems posed will appear in the next issue of AtRiA's problem corner

## AtRiA Set Theory Revisited- As easy as PIE

This article discusses a simple but basic guiding principle which goes under the name 'principle of inclusion and exclusion', or PIE for short.  The principle is very useful indeed, because counting precisely, contrary to intuition, can be very challenging!

## Prime Factorisation

Here is one way of decomposing a number into its prime factors.