Understanding Lcm For 9 And 12

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

What is LCM?

LCM stands for Lowest Common Multiple. It is the smallest number that is a multiple of two or more given numbers. In simpler terms, it is the lowest number that can be divided by two numbers without any remainder.

Finding the LCM of 9 and 12

To find the LCM of 9 and 12, we need to first list down the multiples of each number. The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, and so on. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, and so on.

Method 1: Prime Factorization

One method of finding the LCM is through prime factorization. Prime factorization is the process of breaking down a number into its prime factors. To do this, we need to find the prime factors of both 9 and 12. The prime factors of 9 are 3 and 3, while the prime factors of 12 are 2, 2, and 3. We then write the prime factors in a factor tree: 9 = 3 x 3 12 = 2 x 2 x 3 We then multiply the highest powers of each prime factor to get the LCM. In this case, the highest power of 2 is 2 x 2 = 4, while the highest power of 3 is 3. Therefore, the LCM of 9 and 12 is 4 x 3 = 12.

Method 2: Division Method

Another method of finding the LCM is through the division method. To do this, we write down the numbers in a vertical format and divide them by their common factors, starting with the smallest prime number. 9 | 9 12 - |--- 2 | - | 3 | 1 4 From this, we can see that the LCM of 9 and 12 is 2 x 3 x 3 x 2 = 12.

Importance of LCM

LCM is an important concept in mathematics, as it is used in various fields such as fractions, algebra, and geometry. For example, when adding or subtracting fractions with different denominators, we need to find the LCM of the denominators to make them equivalent.

Conclusion

In conclusion, finding the LCM of 9 and 12 can be done through different methods such as prime factorization and division. Knowing the LCM is important in various mathematical concepts and applications.