Understanding And Solving Lcm For 9 And 24

LCM of 9 and 24 How to Find LCM of 9, 24? from www.cuemath.com

What is LCM?

LCM stands for Least Common Multiple. It is the smallest positive integer that is a multiple of two or more numbers. For example, the LCM of 4 and 6 is 12 because 12 is the smallest number that is divisible by both 4 and 6.

Why is LCM important?

LCM is important in many areas of mathematics, including fractions, decimals, and algebra. It is used to simplify fractions by finding a common denominator, and it is also used to solve equations involving fractions. In addition, LCM is used to find the period of repeating decimals and to solve problems in geometry and physics.

How to find LCM?

To find the LCM of two numbers, you can use the prime factorization method. First, find the prime factors of each number. Then, write down the factors that are common to both numbers, and multiply them together. Finally, multiply the remaining factors to get the LCM.

Prime Factorization Method for 9 and 24

To find the LCM of 9 and 24, we need to write them in their prime factorization form. 9 = 3 x 3 24 = 2 x 2 x 2 x 3 Next, we write down the factors that are common to both numbers. In this case, the common factor is 3. 3 Then, we multiply the common factor with the remaining factors. 2 x 2 x 2 x 3 Finally, we get the LCM by multiplying the common factor with the remaining factors. 3 x 2 x 2 x 2 = 24 Therefore, the LCM of 9 and 24 is 24.

Why is 24 the LCM?

24 is the LCM of 9 and 24 because it is the smallest number that is divisible by both 9 and 24. In other words, 24 is a multiple of both 9 and 24.

How to check if 24 is the LCM?

To check if 24 is the LCM of 9 and 24, we can use the division method. We divide 24 by each number and check if the remainder is 0. 24 ÷ 9 = 2 remainder 6 24 ÷ 24 = 1 remainder 0 Since the remainder is 0 in both cases, we can conclude that 24 is indeed the LCM of 9 and 24.

Conclusion

In conclusion, LCM is an important concept in mathematics that is used to simplify fractions, solve equations, and solve problems in various fields. To find the LCM of two numbers, we can use the prime factorization method. In the case of 9 and 24, the LCM is 24 because it is the smallest number that is divisible by both numbers. We can check if 24 is the LCM by using the division method.