In this article, we explore what LCM is, how to find it, and why it’s important, with a focus on the question, “what is the lcm of 6 and 8?
Are you struggling to find the LCM of 6 and 8? Well, you’re not alone. Many students find the concept of Least Common Multiple (LCM) confusing, but don’t worry, in this article, we’ll explore what LCM is, how to find it, and why it’s important.
Introduction to LCM
Before we dive into finding the LCM of 6 and 8, let’s first understand what LCM is. LCM stands for Least Common Multiple, which is the smallest positive integer that is a multiple of two or more numbers. In simple terms, it’s the smallest number that can be divided by two or more given numbers without leaving any remainder.
For example, the LCM of 2 and 3 is 6 because 6 is the smallest number that is divisible by both 2 and 3 without leaving any remainder. Similarly, the LCM of 4, 6, and 8 is 24 because 24 is the smallest number that is divisible by all three numbers without leaving any remainder.
What are 6 and 8?
Now that we have a basic understanding of LCM, let’s focus on the given numbers, 6 and 8.
Properties of 6
The number 6 is an even composite number. It has four factors: 1, 2, 3, and 6. It’s also the product of 2 and 3, which means it’s divisible by both 2 and 3 without leaving any remainder.
Properties of 8
The number 8 is also an even composite number. It has four factors: 1, 2, 4, and 8. It’s the product of 2 and 4, which means it’s divisible by both 2 and 4 without leaving any remainder.
Now that we know the properties of both numbers, it’s time to find their LCM.
How to find the LCM of 6 and 8
To find the LCM of 6 and 8, we need to understand two methods: prime factorization and division method.
Prime Factorization Method
The prime factorization method is the most common and straightforward method to find the LCM of two or more numbers. Here’s how you can use it to find the LCM of 6 and 8:

Write down the prime factorization of each number.
 Prime factorization of 6: 2 x 3
 Prime factorization of 8: 2 x 2 x 2

Write down the factors that appear in either number, using the highest power for repeated factors.
 Factors: 2 x 2 x 2 x 3

Multiply the factors from step 2.
 LCM of 6 and 8: 2 x 2 x 2 x 3 = 24
Therefore, the LCM of 6 and 8 is 24.
Division Method
The division method is another way to find the LCM of two or more numbers. Here’s how you can use it to find the LCM of 6 and 8:

Write down the two numbers, 6 and 8.

Divide both numbers by the smallest prime number that divides either of the numbers.
 Divide both numbers by 2, which gives 3 and 4.

Divide any of the remaining numbers by the smallest prime number that divides either of the numbers.
 Divide 4 by 2, which gives 2.

You should now have a list of prime factors and their powers. Multiply all the prime factors together to get the LCM.
 LCM of 6 and 8: 2 x 2 x 2 x 3 = 24
Why is finding the LCM important?
Finding the LCM is an essential concept in mathematics. It’s used in various mathematical operations, such as addition and subtraction of fractions with different denominators.
Besides mathematics, LCM has reallife applications in fields such as computer science, engineering, and economics. For instance, in computer science, LCM is used to determine the memory requirements of a computer program. In engineering, LCM is used to find the least common multiple of two or more periodic events, such as the rotation of gears. In economics, LCM is used to find the time when two or more investments will have the same value.
In conclusion, knowing how to find the LCM of numbers is not only important in mathematics but also has practical applications in various fields. Therefore, it’s a concept that every student and professional should understand.
Why is finding the LCM important?
You may be wondering why finding the LCM is important. Well, LCM has several reallife applications, especially in mathematics and science. For instance, when working with fractions, finding the LCM is essential to simplify them. In addition, finding the LCM is crucial when adding or subtracting fractions with different denominators.
Moreover, LCM is also used in finding the period of a repeating decimal. For example, the decimal representation of 1/7 is 0.142857142857… Here, we can see that 142857 repeats after six digits. Thus, the period of the repeating decimal is six, which is the LCM of 7 and 10.
Conclusion
In conclusion, the LCM of 6 and 8 is 24. We arrived at this answer by finding the multiples of 6 and 8 until we found a common multiple, which is 24.
LCM is an essential concept in mathematics and science. It’s the smallest positive integer that is a multiple of two or more numbers. Finding the LCM is crucial when working with fractions, adding or subtracting fractions with different denominators, and finding the period of a repeating decimal.
I hope this article has helped you understand what LCM is, how to find it, and why it’s important. Remember, practice makes perfect, so keep solving problems to improve your LCM skills.