The Lcm Of 8 And 10: Explanation And Solution

LCM of 8 and 10 How to Find LCM of 8, 10? from www.cuemath.com

What is 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, it is the smallest number that is divisible by two or more given numbers without leaving a remainder.

How to Find the LCM of 8 and 10?

To find the LCM of 8 and 10, there are several methods that you can use. One of the most common methods is to list the multiples of each number and find the smallest multiple that they share in common. Here's how to do it:

1. List the multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80,...

2. List the multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,...

3. Find the smallest multiple that they share in common: 40.

Therefore, the LCM of 8 and 10 is 40.

Why is 40 the LCM of 8 and 10?

To understand why 40 is the LCM of 8 and 10, you need to know some basic math concepts. First of all, 8 and 10 are both even numbers, which means that they are divisible by 2. Therefore, any multiple of 8 or 10 will also be divisible by 2.

Now, let's look at the multiples of 8 and 10 again:

1. Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80,...

2. Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,...

You can see that the first multiple that they share in common is 40. This is because 40 is the smallest number that is divisible by both 8 and 10. In other words, 40 is the first common multiple of 8 and 10.

Other Methods to Find the LCM of 8 and 10

Besides listing the multiples, there are other methods that you can use to find the LCM of 8 and 10. One of them is the prime factorization method, which involves breaking down each number into its prime factors and multiplying the highest powers of each factor.

Here's how to use the prime factorization method to find the LCM of 8 and 10:

1. Prime factorization of 8: 2 x 2 x 2 = 2^3

2. Prime factorization of 10: 2 x 5 = 2^1 x 5^1

3. Multiply the highest powers of each factor: 2^3 x 5^1 = 40

Therefore, the LCM of 8 and 10 is 40.

Why is the LCM of 8 and 10 Useful?

The LCM of 8 and 10 is useful in many real-life situations, such as when you need to find a common denominator for two fractions with different denominators. The LCM is also used in algebra, where it helps to simplify equations and solve problems involving rational expressions.

Conclusion

In conclusion, the LCM of 8 and 10 is 40. This is the smallest number that is divisible by both 8 and 10 without leaving a remainder. You can find the LCM of two numbers by listing their multiples or using the prime factorization method. The LCM is a useful concept in math that has many practical applications.