Least Common Multiple

The Least Common Multiple (LCM) of two or more numbers is the smallest positive number that is a multiple of all of them. Mathematically, if we have two numbers \(a\) and \(b\), their LCM is defined as:

\[ \text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)} \]

where \(\text{GCD}(a, b)\) is the Greatest Common Divisor.

Visualization of the LCM

The GeoGebra construction provides a graphical and intuitive way to understand this concept. By representing multiples on a grid or a number line, students can observe how multiples of different numbers coincide at certain points, making it easier to identify the LCM.

Importance of LCM in Mathematical Learning

The concept of LCM is fundamental in various areas of mathematics, including: - Arithmetic and fractions: It facilitates the addition and subtraction of fractions with different denominators. - Algebra: It is used in equations and problems involving fractional expressions. - Real-life applications: It appears in problems related to event synchronization, scheduling, and repeating cycles.

Using a visual representation allows students to better understand this abstract concept and relate it to practical situations, enhancing