The Least Common Multiple Of 10 And 18

LCM of 10 and 18 How to Find LCM of 10, 18? from www.cuemath.com

Introduction

In mathematics, the least common multiple (LCM) is defined as the smallest positive integer that is divisible by two or more given integers without any remainder. It is an important concept used in various mathematical operations, including algebra, geometry, and calculus. In this article, we will discuss the LCM of 10 and 18 and how to calculate it.

The Prime Factorization Method

One of the most popular methods to find the LCM of two numbers is the prime factorization method. This method involves finding the prime factors of each number and then multiplying the highest power of each factor to get the LCM. To find the prime factors of 10, we can divide it by the smallest prime number, which is 2. We get 5 as the quotient. Since 5 is a prime number, we stop here. Therefore, the prime factorization of 10 is 2 x 5. To find the prime factors of 18, we can also start with 2 as the smallest prime number. Dividing 18 by 2 gives us 9 as the quotient. Dividing 9 by 3 gives us 3 as the quotient, which is also a prime number. Therefore, the prime factorization of 18 is 2 x 3 x 3.

The LCM Calculation

To get the LCM using the prime factorization method, we need to multiply the highest power of each factor. In this case, we have 2, 3, and 5 as our factors. From the prime factorization of 10, we can see that 2 has a power of 1 and 5 has a power of 1. From the prime factorization of 18, we can see that 2 has a power of 1 and 3 has a power of 2. To get the LCM, we multiply the highest power of each factor. Therefore, LCM (10, 18) = 2 x 3^2 x 5 = 90.

Conclusion

In conclusion, the LCM of 10 and 18 is 90. We calculated it using the prime factorization method, which involves finding the prime factors of each number and then multiplying the highest power of each factor. This method is useful for finding the LCM of any two or more numbers. Understanding the concept of LCM is crucial in various mathematical operations and can help students excel in their studies.