At times, we’re stuck in situations that require us to break down numbers in their smallest part because that whole number can not be used as it is in that particular situation. The term “factors” come into the picture here. A factor in maths is a number that divides a number completely leaving no remainder behind. LCM and HCF are two such concepts that are based on this building block called factors.
These two mathematical concepts are often used in everyday life, even if we don’t realize it. LCM, or the lowest common multiple, is the smallest number that two or more numbers can be divided into evenly. Whereas, HCF, or the highest common factor, is the largest number that two or more numbers can be divided into evenly. In many real-life situations, such as finding out how much paint to buy for a wall or how many people can fit in a car, it’s necessary to know both the LCM and HCF of a set of numbers.
However, learning about LCM and HCF can be a little dry, but when you see how they are used in the “real world” it becomes a lot more interesting. In this post, we will give some examples of how LCM and HCF are used outside of the classroom.
Comprehending the real-life essence of LCM and HCF
HCF and LCM are fundamental building blocks in many arithmetic areas. Once a student understands this concept well, they can easily jump to more complex topics.
Hence, comprehending the optimum uses of these concepts in real life to understand the concept and the idea can help students learn them better. Let’s have a look at a few everyday examples we come across while using HCF and LCM.
1. Traffic Signals and controllers
The traffic light we see on road avidly exercises the concept of LCM and HCF. The controller sets the timings of the traffic signals in such a way that all the lights are not lighting up at one time; especially during peak hours. Hence, the controller of these traffic signals is set in a way that it calculates the timings of the nearby places in the same area and then calculates the LCM of all the traffic stops to set the timing for each signal. This way, the traffic can move easily, without any chaos.
2. Helps in solving fractions
The fundamental notion of LCM is useful in math for solving fractions. To solve fractions with different denominators, we must bring them both to the same denominator. This involves first bringing them together by utilizing LCM to find a common denominator. Therefore, it becomes crucial for a student to ace fractions in order to better grasp LCM and HCF as a whole.
LCM of significant prime integers is also used in RSA encryption methods for safely transmitting data over internet connections. This is one of the most efficient uses of LCM in the technology and data space. In data security, encryption is the process of transforming readable data into an unreadable format.
This is done using a key, which is a string of bits generated by an algorithm. The key is used to encrypt the data, and the same key is used to decrypt the data. One way to generate a long key is to use the least common multiple (LCM) and highest common factor (HCF) of two large numbers. This method is called LCM-HCF Encryption.
4. Precise Estimation
LCM and HCF can help in the Precise Estimation of everyday activities in the following ways:
- If a professor has three classes, and each of the classes has 28, 42, and 56 students respectively, the professor now wants to divide the class into groups so that every group in every class has the same number of students, and none of them is left over. This might be for some activity that the professor wants to conduct. Hence, by finding the HCF here, of 18, 24, and 42, the professor would be able to get the answer to the number of students to be put in each group.
- They also help in finding how much of an item is required when replication is involved.
- HCF can also be used in finding how long it will take to complete a task when working with a team. For instance, if it takes Alex 2 hours to mow the lawn and it takes Brian 3 hours to do the same job, the HCF of 2 and 3 is 1. This means that it will take 1 hour for both of them to finish mowing the lawn together.
Thus, we can see that LCM and HCF are useful in estimation activities in our daily lives.
5. To help Distribute equally
Distribution of things can be an easy process if done using the concepts of LCM and HCF. For example, if someone has two pieces of cloth, one piece is 45 inches wide and the other is 90 inches wide, how should the person cut the cloth so that there is an equal division of the cloth? Hence, by using HCF here, the individual can easily divide the strips of cloth into small pieces (fractions) of 45 and 90, which are common. Now, all they need to do is, calculate!
When HCF of 45 and 90 is calculated, the answer that comes would be 45, hence, the individual can cut the pieces into 45 inches wide each, to get to their answer.
6. Resource optimization to ensure zero wastage
LCM and HCF are important mathematical concepts that can be used to help optimize resources and prevent wastage. Here’s how they work. HCF can be used to determine the number of square napkins that can be cut from a single sheet of fabric of a specific width and length for all pieces without discarding or wasting any fabric. If you look around and notice, the use of HCF on any given day is vast and so common that we tend to not even realize it.
7. Arranging and sorting
LCM and HCF can help in Arranging items in rows and groups. How? LCM is the lowest common multiple of two or more numbers, while HCF is the highest common factor. LCM can be used to arrange items in rows, while HCF can be used to group items together. For example, if ten items are arranged in rows of five, the LCM of 5 and 10 would be used. Thus LCM and HCF can be useful in arranging items in rows or groups.
Learning the concepts of LCM and HCF comes in handy when pursuing higher education in Mathematics and other relevant subjects. A conceptual understanding of these concepts can be very useful in planning, estimating, and dividing things. If taught in the right manner, children can grasp this concept from the very beginning and keep getting better with practice.
Some mathematical concepts, such as LCM, HCF, and GCF, can be a little tricky for students to grasp. However, incorporating a game-based educational environment can drastically change how they approach the subject. It would pave the path for strong basics that, if correctly learned, would last a lifetime. This also includes introducing these topics with their real-life applications.