The Lcm Of 6 And 21: Explanation And Solution

LCM of 6 and 21 How to Find LCM of 6, 21? from www.cuemath.com

Introduction

In mathematics, the LCM or Least Common Multiple of two or more numbers is the smallest number that is a multiple of all the given numbers. In this article, we will focus on finding the LCM of 6 and 21.

Factors

Before we proceed, let us first determine the factors of these two numbers. The factors of 6 are 1, 2, 3, and 6. The factors of 21 are 1, 3, 7, and 21.

Method 1: Listing Multiples

One way to find the LCM of 6 and 21 is to list down their multiples until we find the smallest number that is common to both lists. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, and so on. The multiples of 21 are 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, and so on. We can see that 42 is the smallest number that appears in both lists. Hence, the LCM of 6 and 21 is 42.

Method 2: Prime Factorization

Another way to find the LCM of 6 and 21 is to use prime factorization. We can express 6 as 2 x 3 and 21 as 3 x 7. Since both numbers have a factor of 3, we only need to include it once in our LCM. We also need to include the factors that are unique to each number, which are 2 and 7. Therefore, the LCM of 6 and 21 is 2 x 3 x 7, which is equal to 42.

Why the LCM is important

The LCM is an important concept in mathematics because it is used in many different applications such as finding equivalent fractions, adding and subtracting fractions with different denominators, and solving algebraic equations. It is also used in real-life situations such as scheduling, where we need to find the smallest time interval that can accommodate multiple events or tasks.

Conclusion

In conclusion, the LCM of 6 and 21 is 42. We can find it by listing down their multiples or by using prime factorization. The LCM is an important concept in mathematics and has many practical applications.