Understanding The Least Common Multiple Of 12 And 5

Ex 3.7, 10 Find LCM of (a) 9 and 4 (b) 12 and 5 (c) 6 5 (d) 15 4 from www.teachoo.com

What is a Multiple?

Before we dive into the concept of the Least Common Multiple (LCM) of 12 and 5, it is important to understand what a multiple is. A multiple is a product that results from multiplying a number by an integer. For instance, multiples of 5 include 5, 10, 15, 20, and so on.

What is the LCM?

The LCM of two or more numbers is the smallest number that is a multiple of all of the given numbers. In other words, it is the lowest common denominator of the numbers. For instance, the LCM of 3 and 4 is 12 because 12 is the smallest number that is a multiple of both 3 and 4.

How to Find the LCM of 12 and 5

To find the LCM of 12 and 5, there are various methods. One way is to list the multiples of each number and find the smallest number that appears in both lists. Multiples of 12 include 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so on. Multiples of 5 include 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, and so on. From the lists, we can see that 60 is the smallest number that appears in both lists. Therefore, the LCM of 12 and 5 is 60.

Prime Factorization Method

Another way to find the LCM of 12 and 5 is through the prime factorization method. This method involves finding the prime factors of each number and multiplying them together. The prime factors of 12 are 2, 2, and 3. The prime factors of 5 are 5. To find the LCM, we multiply the highest powers of each prime factor. In this case, the highest power of 2 is 2^2, the highest power of 3 is 3^1, and the highest power of 5 is 5^1. Multiplying these together gives us 2^2 x 3 x 5, which simplifies to 60.

Why is the LCM Important?

The LCM is an important concept in mathematics because it is used in various calculations, such as adding and subtracting fractions. When adding or subtracting fractions, we need to find the lowest common denominator (LCD), which is essentially the LCM of the denominators. For example, to add 1/3 and 1/4, we need to find the LCD of 3 and 4, which is 12. We then convert each fraction to have a denominator of 12 and add them together. The result is 7/12.

Conclusion

In summary, the LCM of 12 and 5 is 60, which is the smallest number that is a multiple of both 12 and 5. There are various methods to find the LCM, such as listing the multiples or using the prime factorization method. The LCM is an important concept in mathematics that is used in various calculations involving fractions.