Understanding The Least Common Multiple Of 12 And 9

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Introduction

The concept of Least Common Multiple (LCM) is often taught in middle school mathematics. It is an important concept that helps solve problems related to fractions, ratios, and proportions. In this article, we will discuss what LCM is and how to find the LCM of 12 and 9.

What is LCM?

LCM is the smallest multiple that two or more numbers have in common. In other words, it is the smallest number that is divisible by both 12 and 9 without leaving any remainder. LCM is often used in real-life situations, such as finding the least common denominator while adding or subtracting fractions.

Finding the LCM of 12 and 9

There are different methods to find the LCM of two numbers, but the most common method is the prime factorization method. In this method, we factorize the given numbers into prime factors and then multiply the highest power of each prime factor to get the LCM.

Prime factorization of 12

To factorize 12 into prime factors, we can divide it by the smallest prime number, which is 2. We repeat this process until we get 1. 12 ÷ 2 = 6 6 ÷ 2 = 3 3 is a prime number, so we stop here. Therefore, the prime factorization of 12 is 2 x 2 x 3.

Prime factorization of 9

To factorize 9 into prime factors, we can divide it by the smallest prime number, which is 3. We repeat this process until we get 1. 9 ÷ 3 = 3 3 is a prime number, so we stop here. Therefore, the prime factorization of 9 is 3 x 3.

Multiplying the highest power of each prime factor

To find the LCM of 12 and 9, we need to multiply the highest power of each prime factor. In this case, the prime factors are 2 and 3. The highest power of 2 is 2 x 2 = 4, and the highest power of 3 is 3 x 3 = 9. Therefore, the LCM of 12 and 9 is 4 x 9 = 36.

Conclusion

In conclusion, the LCM of 12 and 9 is 36. It is important to understand the concept of LCM as it helps in solving various mathematical problems. The prime factorization method is the most efficient way to find the LCM of two or more numbers.