What Is Lcm Of 7 And 8?

LCM of 7 and 8 How to Find LCM of 7, 8? from en.asriportal.com

Introduction

Finding the LCM of two numbers is a common problem in mathematics. LCM stands for the Least Common Multiple. It is the smallest positive integer that is divisible by both numbers without leaving a remainder. In this article, we will discuss the LCM of 7 and 8.

Factors of 7 and 8

Before finding the LCM, we need to determine the factors of both numbers. The factors of 7 are 1 and 7, while the factors of 8 are 1, 2, 4, and 8.

Method 1: Listing Multiples

One way to find the LCM of 7 and 8 is to list their multiples until we find the smallest one that they have in common. The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, and so on. We can see that 56 is the smallest multiple that they have in common. Therefore, the LCM of 7 and 8 is 56.

Method 2: Prime Factorization

Another way to find the LCM of 7 and 8 is to use prime factorization. We can express both numbers as a product of their prime factors. The prime factors of 7 are only 7, while the prime factors of 8 are 2 x 2 x 2.

Step 1: Prime Factorization

7 = 7 x 1 8 = 2 x 2 x 2

Step 2: Identify Common Factors

Next, we need to identify the common factors and the uncommon factors. We can see that 2 is a common factor, but 7 is not.

Step 3: Multiply Common and Uncommon Factors

Finally, we need to multiply the common factors and the uncommon factors. The common factor is 2, so we multiply it once. The uncommon factors are 7 and 2 x 2, so we multiply them once each. 2 x 2 x 2 x 7 = 56 Therefore, the LCM of 7 and 8 is 56, which is the same as the answer we obtained using the first method.

Conclusion

In conclusion, the LCM of 7 and 8 is 56. We can find it by listing their multiples or by using prime factorization. LCM is an important concept in mathematics, and it has many applications in real-life situations such as scheduling, fractions, and ratios.