Contextualization
As one of the oldest disciplines, Mathematics concerns itself with organization, structure, and quantities. One of Mathematics' subdisciplines focuses on whole numbers and their properties, known as Arithmetic. Among the most important topics in Arithmetic is the concept of the Least Common Multiple (LCM).
The LCM is a powerful tool for solving problems involving the set of whole numbers. It is the smallest whole number that can be divided without remainder by each of the numbers in a given set. It helps us to better understand the concept of divisibility and is fundamental for solving problems that require us to equate multiples of different numbers.
In the real world, the LCM is applied in various contexts. When we work with time, for example, the LCM helps us to determine when periodic events will coincide again. If you have an alarm that goes off every 3 hours and another that goes off every 5, when will they go off at the same time? The answer is given by the LCM of 3 and 5, which is 15. Therefore, the alarms will go off together every 15 hours.
Furthermore, the LCM also plays an important role when we work with fractions, which are present in various situations in our daily lives. Imagine that you are cooking and need to add fractions with different denominators; the LCM will be useful for finding a common denominator.
To support the study of LCM, we recommend the following resources:
- SOS Professor: is an excellent resource for understanding the basic concepts of LCM.
- Khan Academy: has explanatory videos and exercises that help to deeply understand the topic.
- The book "Elementary Mathematics: Whole Numbers and Combinatorics" by Gelson Iezzi: is a more detailed resource for those who wish to understand even more about the topic.
Practical Activity: LCM Challenge
Project Objective
The objective of this project is to understand the concept of Least Common Multiple (LCM), to apply this concept in the addition and subtraction of fractions, and in solving everyday problems. At the end of the project, students will be able to calculate the LCM of two or more numbers, to use the LCM to add/subtract fractions, and to solve everyday problems that involve LCM.
Detailed Project Description
The students, organized into groups of 3 to 5, will work on a hands-on challenge that involves applying LCM in everyday situations. Together, we will decide on a social cause for which we will hold a bazaar. To do this, each student will bring a certain quantity of an item, which will be sold in the quantity that represents the LCM of the items brought.
Necessary materials
- Paper;
- Pens;
- Calculator;
- Computer with internet access (optional).
Step-by-step guide for carrying out the activity
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Group Formation: Students will group themselves into teams of 3 to 5. Each team must appoint a leader who will be responsible for organizing and coordinating the group's activities.
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Study on LCM: Students will study the concepts of LCM using the suggested resources or other materials of their choice. They must understand the concept, know how to calculate the LCM of two or more numbers, and understand how the LCM is used to add and subtract fractions.
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Bazaar Planning: Each student in the group will bring a different quantity of the same item to be sold at the bazaar (for example, each student can bring a different quantity of T-shirts, books, etc.). The item to be sold and the quantities will be decided by the groups.
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Challenge Solution: Students must calculate the LCM of the quantities of items brought. They must then decide how many units of each item will be sold at the bazaar, and this number must be a common multiple of the quantities brought.
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Project Report: At the end of the project, each group will write a report containing the following sections: Introduction, Development, Conclusions, and Bibliography.
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Project Presentation: The groups will present their work to the class, explaining the concept of LCM, the methodology used, the solution to the challenge, and the conclusions reached.
Project Deliverables
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Study on LCM: In the first stage, each group must share a summary of what they learned about LCM. This summary should be included in the Development section of the report.
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Bazaar Challenge: In the second stage, the groups must explain how they calculated the LCM and the decision made about how many units of each item will be sold at the bazaar. This discussion should be included in the Development section of the report.
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Project Report: Each group must submit a written report with the following sections: Introduction (contextualization of the topic and project objective), Development (explanation of the concept of LCM, detailed description of the activity carried out, explanation of the methodology used, and presentation of the results), Conclusion (recalling the main points of the work and explaining what was learned and the conclusions about the project), and Bibliography (with all of the sources consulted).
Each section of the report is essential and complements the practical work carried out. The introduction should contextualize the topic and show its relevance both in mathematics and in practical applications. The development is the densest and most detailed part of the report, where the students will explain the theory of LCM, a detailed description of the practical activity, and the reasoning behind the decisions made. In the conclusion, the students should reflect on what they learned and the experience acquired throughout the project. The bibliography is where the students cite the research sources that supported the development of the project.
- Project Presentation: Each group will give a presentation of the project to the class. In this presentation, the groups should not only explain the concept of LCM and the solution to the challenge, but also discuss the conclusions reached and the teamwork process.
