Lcm For 24 And 30

LCM of 24 and 30 How to Find LCM of 24, 30? from www.cuemath.com

Introduction

Finding the LCM (Least Common Multiple) of two numbers is a common mathematical problem that many students come across in their academic journey. LCM is an important concept as it is used in various mathematical operations, including fractions, addition, and subtraction of fractions. In this article, we will discuss how to find the LCM of 24 and 30. We will explain the concept of LCM, its importance, and the step-by-step process of finding the LCM for 24 and 30.

What is LCM?

LCM stands for Least Common Multiple, which is the smallest positive integer that is a multiple of two or more numbers. In simple terms, LCM is the smallest number that two or more numbers can be divided by without leaving any remainder. For example, the LCM of 3 and 5 is 15 because 15 is the smallest number that 3 and 5 can be divided by without leaving any remainder. Similarly, the LCM of 4, 6, and 8 is 24 because 24 is the smallest number that all three numbers can be divided by without leaving any remainder.

Why is LCM important?

LCM is an important concept in mathematics, particularly in fractions. When adding or subtracting fractions with different denominators, we need to find the LCM of the denominators to make the fractions equivalent. For example, to add 1/3 and 1/4, we need to find the LCM of 3 and 4, which is 12. We then convert 1/3 and 1/4 into fractions with a denominator of 12, which gives us 4/12 and 3/12. We can then add these fractions to get 7/12.

How to find the LCM of 24 and 30?

To find the LCM of 24 and 30, we need to follow the following steps: Step 1: Write down the prime factorization of each number 24 = 2^3 x 3 30 = 2 x 3 x 5 Step 2: Write down the factors of each number The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. Step 3: Identify the common factors The common factors of 24 and 30 are 1, 2, 3, and 6. Step 4: Multiply the common factors The product of the common factors is 1 x 2 x 3 x 6 = 36. Step 5: Include the remaining factors We need to include the remaining factors that are not common in both numbers. These are 2^2 and 5. Step 6: Multiply all the factors The LCM of 24 and 30 is the product of all the factors, which is 2^3 x 3 x 5 = 120. Therefore, the LCM of 24 and 30 is 120.

Conclusion

In conclusion, finding the LCM of two numbers is an important concept in mathematics, particularly in fractions. The LCM is the smallest positive integer that is a multiple of two or more numbers. To find the LCM of 24 and 30, we need to follow the above steps, which involve finding the prime factorization of each number, identifying the common factors, and multiplying all the factors. By following these steps, we can find the LCM of any two numbers.