What Is The Least Common Multiple Of 4 And 10?

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Introduction

As a math teacher, one of the most important concepts that I teach my students is the idea of finding the least common multiple (LCM) of two numbers. In this article, we will explore the process of finding the LCM of 4 and 10, and provide a step-by-step solution that anyone can understand.

What is a Multiple?

Before we dive into finding the LCM of 4 and 10, it is important to understand what a multiple is. A multiple of a number is the product of that number and any other whole number. For example, 4 is a multiple of 2 because 2 x 2 = 4. Similarly, 10 is a multiple of 5 because 5 x 2 = 10.

What is the Least Common Multiple?

The least common multiple of two numbers is the smallest number that is a multiple of both of them. For example, the LCM of 4 and 10 is the smallest number that is both a multiple of 4 and a multiple of 10.

How to Find the LCM of 4 and 10

To find the LCM of 4 and 10, we can use a method called prime factorization. This method involves breaking each number down into its prime factors and then multiplying the highest power of each factor together.

Step 1: Find the Prime Factors

The first step in finding the LCM of 4 and 10 is to find the prime factors of each number. The prime factors of 4 are 2 x 2, and the prime factors of 10 are 2 x 5.

Step 2: Identify the Highest Power of Each Factor

The next step is to identify the highest power of each factor. In this case, the highest power of 2 is 2 x 2, and the highest power of 5 is 5. Therefore, the LCM of 4 and 10 is 2 x 2 x 5, which equals 20.

Why is the LCM of 4 and 10 20?

The LCM of 4 and 10 is 20 because it is the smallest number that is a multiple of both 4 and 10. 20 is a multiple of 4 because 4 x 5 = 20, and it is a multiple of 10 because 10 x 2 = 20. Therefore, 20 is the least common multiple of 4 and 10.

Conclusion

In conclusion, finding the least common multiple of 4 and 10 requires breaking each number down into its prime factors and then multiplying the highest power of each factor together. By following the steps outlined in this article, anyone can find the LCM of any two numbers.