The Lcm Of 16 And 20

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

Understanding LCM

LCM stands for Least Common Multiple. It is the smallest number that is a multiple of two or more given numbers. In other words, LCM is the lowest common denominator of two or more numbers. It is used in many mathematical operations, such as adding or subtracting fractions, simplifying algebraic expressions, and solving equations.

Prime Factorization Method

One of the most common methods to find the LCM of two numbers is the prime factorization method. This method involves breaking down each number into its prime factors, then multiplying the highest power of each prime factor. For example, to find the LCM of 16 and 20, we need to first factorize them into their prime factors.

Prime Factorization of 16

16 can be written as 2 x 2 x 2 x 2 or 2^4. This means that 16 is the product of four 2s.

Prime Factorization of 20

20 can be written as 2 x 2 x 5 or 2^2 x 5. This means that 20 is the product of two 2s and one 5.

Multiplying the Highest Power of Each Prime Factor

To find the LCM of 16 and 20, we need to multiply the highest power of each prime factor. In this case, the prime factors are 2 and 5. Since 16 has four 2s and 20 has two 2s, we need to take the highest power of 2, which is 2^4. Since 20 has one 5, we take 5^1. Therefore, the LCM of 16 and 20 is 2^4 x 5^1, which is 80.

Verification

To verify our answer, we can check if 80 is a multiple of both 16 and 20. 80 is a multiple of 16 because 80/16 = 5. 80 is also a multiple of 20 because 80/20 = 4. Therefore, 80 is the LCM of 16 and 20.

Conclusion

In conclusion, the LCM of 16 and 20 is 80. This is the smallest number that is a multiple of both 16 and 20. The prime factorization method is a useful tool in finding the LCM of two or more numbers. It is important to understand LCM because it is used in many mathematical operations.