Understanding Lcm Of 21 And 14

LCM of 14 and 21 How to Find LCM of 14, 21? from www.cuemath.com

Introduction

LCM stands for Lowest Common Multiple. It is a mathematical term used to find the smallest number that is divisible by two or more numbers without leaving any remainder. In this case, we are finding out the LCM of 21 and 14.

Method to Find LCM

To understand how to find the LCM of 21 and 14, we need to know a few basic concepts. Firstly, we need to know the prime factors of each number. Prime factors are the factors that are prime numbers. For example, the prime factors of 21 are 3 and 7, whereas the prime factors of 14 are 2 and 7. Once we have the prime factors, we need to find the highest power of each factor that appears in either number. We then multiply these factors together to get the LCM.

Prime Factors of 21 and 14

As mentioned earlier, the prime factors of 21 are 3 and 7. The prime factors of 14 are 2 and 7.

Finding the Highest Power of Each Factor

Now that we know the prime factors of both numbers, we need to find the highest power of each factor. The highest power of 3 in 21 is 1, and the highest power of 3 in 14 is 0. Therefore, we take 3^1 in our calculation. Similarly, the highest power of 2 in 21 is 0, and the highest power of 2 in 14 is 1. Therefore, we take 2^1 in our calculation. Finally, the highest power of 7 in 21 is 1, and the highest power of 7 in 14 is 1. Therefore, we take 7^1 in our calculation.

Calculation of LCM

To calculate the LCM of 21 and 14, we multiply the highest power of each factor. Therefore, the LCM of 21 and 14 is 2^1 x 3^1 x 7^1, which equals 42.

Conclusion

In conclusion, the LCM of 21 and 14 is 42. To find the LCM of any two numbers, we need to find the prime factors of each number, identify the highest power of each factor present in either number, and multiply these factors together.