Understanding And Solving Lcm Of 24 And 32

LCM of 24 and 32 How to Find LCM of 24, 32? from www.cuemath.com

Introduction

Least Common Multiple or LCM is an essential mathematical concept that is widely used in various fields, including engineering, science, and business. It is defined as the smallest multiple that two or more numbers have in common. In this article, we will discuss how to find the LCM of 24 and 32.

Factors of 24 and 32

Before we proceed with finding the LCM of 24 and 32, we must first determine their factors. Factors are numbers that can be multiplied together to obtain the original number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, while the factors of 32 are 1, 2, 4, 8, 16, and 32.

Finding the LCM of 24 and 32

There are several methods to find the LCM of two numbers, including prime factorization, listing multiples, and the ladder method. In this article, we will discuss the ladder method. To find the LCM of 24 and 32 using the ladder method, we will start by writing down the two numbers and their common factors. Next, we will draw a vertical line to the right of the numbers and list their prime factors on the left side of the line.

24 | 2

32 | 2

We can see that both 24 and 32 have a common factor of 2. We will write this factor on the right side of the line and divide both numbers by 2. The new numbers are 12 and 16.

24 | 2

12 | 2

32 | 2

16 | 2

| 2

We will repeat the process of dividing the numbers by their common factors until we reach a point where they have no more common factors. The next common factor is 2 again, so we will list it on the right side of the line and divide 12 and 16 by 2 again. The new numbers are 6 and 8.

24 | 2

12 | 2

6 | 2

32 | 2

16 | 2

8 | 2

| 2

We will repeat the process until we reach a point where the two numbers have no more common factors. The next common factor is 2 again, so we will list it on the right side of the line and divide 6 and 8 by 2 again. The new numbers are 3 and 4.

24 | 2

12 | 2

6 | 2

3 | 3

32 | 2

16 | 2

8 | 2

4 | 2

| 2

We can see that 3 and 4 have no common factors, so we will list them on the right side of the line without dividing. Finally, we will multiply all the numbers on the right side of the line to get the LCM of 24 and 32.

24 | 2

12 | 2

6 | 2

3 | 3

32 | 2

16 | 2

8 | 2

4 | 2

| 2

3 |

4 |

2*2*2*2*3*4 = 96

Therefore, the LCM of 24 and 32 is 96.

Conclusion

In conclusion, finding the LCM of two numbers is essential in various mathematical applications. In this article, we have discussed how to find the LCM of 24 and 32 using the ladder method. It involves listing the numbers and their common factors, dividing the numbers until they have no more common factors, and multiplying all the numbers on the right side of the line. By following this method, we have found that the LCM of 24 and 32 is 96.