Understanding The Least Common Multiple Of 12 And 8

How to Find the LCM of 8 & 12 Video & Lesson Transcript from study.com

Introduction

The least common multiple (LCM) is a value that is commonly used in mathematics to find the smallest common multiple of two or more numbers. In simple terms, it is the smallest number that is a multiple of both numbers. In this article, we will discuss the LCM of 12 and 8 and how to find it.

What is a Multiple?

A multiple is a product of a number and any integer. For example, multiples of 2 are 2, 4, 6, 8, 10, and so on. Multiples of 3 are 3, 6, 9, 12, 15, and so on. Similarly, multiples of 12 are 12, 24, 36, 48, and so on.

What is the LCM of 12 and 8?

To find the LCM of 12 and 8, we need to list down the multiples of both numbers and find the smallest multiple that they have in common. Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, and so on. Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, and so on. From the above lists, we can see that the smallest multiple that both 12 and 8 share is 24. Therefore, the LCM of 12 and 8 is 24.

How to Find the LCM using Prime Factorization?

Another method to find the LCM of two numbers is by using prime factorization. To use this method, we need to find the prime factors of both numbers and then multiply the common and uncommon factors to get the LCM. Prime factors of 12: 2 x 2 x 3 Prime factors of 8: 2 x 2 x 2 To find the LCM, we need to multiply the common factors and the uncommon factors. Common factors: 2 x 2 = 4 Uncommon factors: 3 x 2 x 2 = 12 LCM: 4 x 12 = 48 Therefore, the LCM of 12 and 8 using prime factorization is 48.

Why is LCM important?

LCM is important in various mathematical applications such as adding or subtracting fractions with different denominators, simplifying fractions, solving equations, and finding the period of repeating decimals.

Conclusion

In conclusion, the LCM of 12 and 8 is 24. We can find the LCM by listing down the multiples of both numbers or by using prime factorization. LCM is an important concept in mathematics and has various applications in solving mathematical problems.