What Is The Least Common Multiple Of 6 And 18?

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Introduction

In mathematics, multiples are the products of a given number with any other whole number. For example, the multiples of 6 are 6, 12, 18, 24, 30, and so on. Similarly, the multiples of 18 are 18, 36, 54, 72, and so on. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.

Method 1: Prime Factors

One common method to find the LCM of two numbers is to list down their prime factors and multiply each prime factor the highest number of times it occurs in either number. For example, the prime factors of 6 are 2 and 3, while the prime factors of 18 are 2 and 3 multiplied by 3. Therefore, the LCM of 6 and 18 is 2 x 3 x 3 = 18.

Method 2: Division Method

Another method to find the LCM of two numbers is to use the division method. We start by dividing the larger number by the smaller number. If the remainder is zero, then the smaller number is the LCM. If not, we divide the smaller number by the remainder and continue the process until the remainder is zero. For example, to find the LCM of 6 and 18, we divide 18 by 6 to get a quotient of 3 and a remainder of 0. Therefore, the LCM of 6 and 18 is 6 x 3 = 18.

Using Multiplication Table

A third method to find the LCM of two numbers is to use a multiplication table. We start by writing down the multiples of each number until we find a common multiple. For example, the multiples of 6 are 6, 12, 18, 24, 30, and so on, while the multiples of 18 are 18, 36, 54, 72, and so on. The first common multiple is 18, which means that the LCM of 6 and 18 is 18.

Conclusion

In conclusion, the LCM of 6 and 18 is 18, which means that 18 is the smallest number that is a multiple of both 6 and 18. There are several methods to find the LCM of two numbers, including the prime factorization method, the division method, and the multiplication table method. Each method has its own advantages and disadvantages, and it is up to the individual to choose the method that suits them best.