What Is The Least Common Multiple Of 5 And 8?

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Introduction

In the subject of mathematics, the least common multiple (LCM) is a term that is commonly used. It refers to the smallest number that is a multiple of two or more given numbers. This concept is important in various mathematical calculations and applications. In this article, we will discuss the LCM of 5 and 8 and how to calculate it.

Understanding Multiples

Before we can understand the LCM, it is important to know what multiples are. A multiple is a product of a given integer and any other integer. For example, the multiples of 5 are 5, 10, 15, 20, 25, and so on. Similarly, the multiples of 8 are 8, 16, 24, 32, and so on.

Definition of Least Common Multiple

The LCM is the smallest number that is a multiple of two or more given numbers. For example, the LCM of 5 and 8 is the smallest number that is divisible by both 5 and 8. In this case, the LCM is 40.

Methods for Finding LCM

There are different methods for finding the LCM of two or more numbers. One method is to list the multiples of each number and find the smallest multiple that they have in common. Another method is to use prime factorization.

Listing Multiples

To find the LCM of 5 and 8 using the method of listing multiples, we can start by listing the multiples of 5 and 8 until we find a common multiple. The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, and so on. From this list, we can see that the smallest common multiple of 5 and 8 is 40.

Using Prime Factorization

Another method for finding the LCM of 5 and 8 is to use prime factorization. First, we need to find the prime factors of each number. The prime factors of 5 are 5 and the prime factors of 8 are 2 and 2 and 2. Next, we write the prime factors of each number in exponential form. For example, 5 can be written as 5^1 and 8 can be written as 2^3. Then, we take the highest power of each prime factor and multiply them together. In this case, the LCM of 5 and 8 is 2^3 × 5^1 = 40.

Importance of LCM

The concept of LCM is important in various mathematical calculations such as adding and subtracting fractions with different denominators. To add or subtract fractions with different denominators, we need to find the LCM of the denominators and convert the fractions into equivalent fractions with the same denominator.

Conclusion

The LCM is the smallest number that is a multiple of two or more given numbers. There are different methods for finding the LCM such as listing multiples and using prime factorization. The LCM is an important concept in various mathematical calculations and applications. In the case of 5 and 8, the LCM is 40.