The Least Common Multiple Of 12 And 20

LCM of 12 and 20 How to Find LCM of 12, 20? from www.cuemath.com

Introduction

In mathematics, the least common multiple (LCM) is an important concept that is used to find the smallest multiple of two or more numbers. It is a fundamental concept in arithmetic, and it is used in many different areas of mathematics.

What is the Least Common Multiple?

The least common multiple of two or more integers is the smallest positive integer that is a multiple of each of the given numbers. In other words, it is the smallest number that is divisible by both of the given numbers without leaving any remainder.

How to Find the LCM of 12 and 20?

To find the LCM of 12 and 20, we need to find the smallest number that is divisible by both 12 and 20. One way to find the LCM is to list the multiples of each number until we find the smallest multiple that is common to both.

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ...

Method 1: Listing Multiples

From the list of multiples, we can see that the smallest multiple that is common to both 12 and 20 is 60. Therefore, the LCM of 12 and 20 is 60.

Method 2: Prime Factorization

Another way to find the LCM is to use prime factorization. We can find the prime factors of each number and then multiply the highest powers of each prime factor together.

Prime factors of 12: 2 x 2 x 3

Prime factors of 20: 2 x 2 x 5

The highest power of 2 is 2 x 2 = 4. The highest power of 3 is 3. The highest power of 5 is 5.

LCM = 2 x 2 x 3 x 5 = 60

Why is the LCM Important?

The LCM is important because it is used in many different areas of mathematics, including fractions, ratios, and proportions. When adding or subtracting fractions with different denominators, we need to find the LCM to make the denominators the same. The LCM is also used in solving problems involving ratios and proportions.

Conclusion

In conclusion, the least common multiple of 12 and 20 is 60. The LCM is an important concept in mathematics that is used in many different areas, and it is essential to understand how to find the LCM of two or more numbers.