Understanding The Least Common Multiple Of 9 And 12

LCM of 9 and 12 How to Find LCM of 9, 12? from www.cuemath.com

Introduction

The least common multiple (LCM) is a concept in arithmetic that is used to find the smallest multiple that two or more numbers have in common. It is an important topic that is often taught in schools and is used in various mathematical calculations.

What is the Least Common Multiple of 9 and 12?

To find the LCM of 9 and 12, we need to list the multiples of both numbers and find the smallest one that they have in common. The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, etc. and the multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, etc. From the list, we can see that the smallest multiple that both 9 and 12 have in common is 36. Therefore, the LCM of 9 and 12 is 36.

Why is LCM Important?

LCM is important in various mathematical calculations, such as adding and subtracting fractions with different denominators, simplifying fractions, and solving algebraic equations. It is also used in real-life situations, such as finding the least amount of time it would take for two people to meet or the least amount of material needed to make a certain number of objects.

How to Find LCM?

To find the LCM of two or more numbers, we can use different methods, such as listing the multiples, using prime factorization, or using the ladder method. The ladder method is a simple and efficient way to find the LCM of two or more numbers.

The Ladder Method

The ladder method involves listing the multiples of the given numbers and finding the smallest one they have in common. Here are the steps to use the ladder method: Step 1: Write the numbers to be found the LCM of on the left side of the ladder. Step 2: Write the prime factors of each number above them. Step 3: Find the highest power of each prime factor that appears in any of the numbers and write them on the right side of the ladder. Step 4: Multiply the prime factors on the right side of the ladder to get the LCM.

Example:

To find the LCM of 12, 18, and 24, we can use the ladder method as follows: ``` | 12 | 2^2 * 3 | 18 | 2 * 3^2 | 24 | 2^3 * 3 LCM = 2^3 * 3^2 = 72 ```

Conclusion

In conclusion, the LCM of 9 and 12 is 36, which is the smallest multiple they have in common. LCM is an important concept in arithmetic that is used in various mathematical calculations and real-life situations. We can find the LCM of two or more numbers using different methods, such as listing the multiples, using prime factorization, or using the ladder method.