Many students are often confused about LCM and GCF. These are two essential match topics that set the base for more advanced concepts. That’s why it is essential to know the difference between the greatest common factor and the least common multiple. Understanding how they differ can help students better apply these concepts to different theoretical and practical problems.
In this article, we will walk you through the key differences between GCF and LCM. We will also discuss how and where they are applied for various purposes. However, before delving into the distinctions and applications, let’s start from the basics of both concepts. So, ready to begin? Let’s roll.
What Is GCF?
GCF, or greatest common factor, is the highest number that divides two or more numbers without leaving a remainder. That’s why it is also known as the highest common divisor. When multiple numbers are factored, we get many numbers that are common in all the numbers involved. However, the GCF is only the number that is the greatest among all common factors.
What Is LCM?
LCM is the short term used to represent the least common multiple. It refers to the multiple of two or more numbers that is both smallest and common. In simple words, it is the smallest number, which is a multiple of a group of numbers. In the case of two odd numbers less than 9, the LCM is usually the multiple of both numbers.
Key Differences Between GCF And LCM
Here are the fundamental dissimilarities between GCF and LCM for your clarification:
- Fundamental Distinction: When it comes to finding GCF, we have to factorize the numbers into their components to find the greatest common factor. On the other hand, LCM is dependent on multiples, not factors. So, it aims to identify the lowest multiple that is common in a group of numbers.
- Resultant Number: The number we get after finding GCF is always smaller than all the numbers involved. However, it may also be equal to one of the numbers under observation. Conversely, since LCM is a multiple, its value is always higher than all the numbers whose least count multiple is being found.
- Relation With Co-Prime Numbers: Whether it is two or more co-prime numbers, they share just one common factor, which is 1. So, in this case, the GCF always remains 1. However, for two or more co-prime numbers, the lowest common multiple is simply the product of all the numbers involved.
- Purpose Of Applications: GCF is related to division, so it is usually applied in problems where division is needed. The main purpose of its application is to simplify numbers to their lowest form. On the other hand, LCM is associated with multiplication. However, it is utilized to align and combine two or more intervals by finding the common multiple.
Applications Of GCF (Greatest Common Factor)
The main applications of GCF are listed below:
- Simplifying Fractions: Multiplying and dividing a fraction by the highest common divisor results in the simplest form of a fraction. For instance, the GCF of 12 and 20 is 4, and it will convert the fraction from 12/20 to 3/5.
- Finding Ratios: Just like in the case of fractions, GCF is also applied to ratios to simplify them. By dividing the numbers involved in the ratio by their GCF, we get the simplified ratio. For example, if we divide 25:75 by their GCF 25, the ratio becomes 1:3.
- Solving Geometry Problems: In many geometry problems, students have to divide different shapes into smaller but equal-sized parts. In this regard, GCF helps them to determine the size of the largest possible part.
Applications of LCM (Least Common Multiple)
Here are the most common applications of LCM:
- Adding and Subtracting Fractions: Since fractions are not the whole numbers, they cannot be added or subtracted in an ordinary way. That’s why you have to find the LCM of the denominators of all the fractions to perform addition or subtraction.
- Scheduling Problems: In mathematics, when dealing with events that repeat over different intervals, LCM is used to find the point at which they occur at the same time. This helps you set the intervals of events so that they don’t conflict.
- Finding Common Cycle: The problem associated with the rotation of gears or other similar objects often requires calculating the common cycle. The LCM allows you to find the number of cycles at which the two gears or other rotating materials with teeth coincide or align.
Best Way To Calculate GCF And LCM
When it comes to calculating GCF, we have to list all the prime factors of the intended numbers. Then, you have to circle the factor that comes into all the numbers but is the greatest. In contrast, you are required to list the multiples of the numbers to find their LCM. Similarly, you can spot the lowest multiple that is common in all numbers.
However, in the case of higher numbers, this calculation can extend to a large number of steps, wasting your time and energy. Also, in manual calculations, you may fall victim to errors, requiring you to repeat the process. So, to avoid this hassle, you can use online tools such as the greatest common multiple calculator to make the computation quicker and more accurate.
Wrapping Up
After going through this article, we hope that you have learned how GCF and LCM differ and are applied to different math problems. So, from now on, we hope that you will use these concepts appropriately without any conflict.
