Explanation And Solution For Finding The Lcm Of 16 And 20

LCM of 16 and 20 How to Find LCM of 16, 20? from www.cuemath.com

Introduction

The Least Common Multiple, commonly known as LCM, is a mathematical concept that is used to find the smallest common multiple of two or more numbers. In this article, we will discuss how to find the LCM of 16 and 20.

Prime Factorization

To find the LCM of 16 and 20, we need to first perform the prime factorization of both numbers. Prime factorization is the process of breaking down a number into its prime factors. The prime factorization of 16 is 2 x 2 x 2 x 2 or 2^4, while the prime factorization of 20 is 2 x 2 x 5 or 2^2 x 5.

Identifying Common Factors

Once we have the prime factorization of both numbers, we need to identify the common factors. In this case, the only common factor between 16 and 20 is 2.

Multiplying Common Factors

After identifying the common factors, we need to multiply them. In this case, we only have one common factor, which is 2, so we multiply it once. 2 x 1 = 2

Multiplying Remaining Factors

Next, we need to multiply the remaining factors that are not common to both numbers. For 16, the remaining factor is 2^3, and for 20, the remaining factor is 5. 2^3 x 5 = 40

LCM Formula

Finally, we can use the LCM formula to find the LCM of 16 and 20. The formula for finding the LCM of two numbers is: LCM = (first number x second number) / GCD where GCD stands for Greatest Common Divisor.

Greatest Common Divisor

To find the GCD of 16 and 20, we can use the Euclidean algorithm. The algorithm involves dividing the larger number by the smaller number and taking the remainder. This process is repeated until the remainder is 0. The last non-zero remainder is the GCD. Using this method, we can find that the GCD of 16 and 20 is 4.

Calculating the LCM

Now that we have the GCD, we can use the LCM formula to find the LCM of 16 and 20. LCM = (16 x 20) / 4 LCM = 80 Therefore, the LCM of 16 and 20 is 80.

Conclusion

In conclusion, finding the LCM of 16 and 20 involves performing the prime factorization of both numbers, identifying the common factors, multiplying the common factors, multiplying the remaining factors, finding the GCD using the Euclidean algorithm, and using the LCM formula to calculate the LCM. By following these steps, we can find the LCM of any two numbers.