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7 And 8 Least Common Multiple

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Least Common Multiple
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Introduction

The least common multiple (LCM) is a mathematical concept that is used to find the smallest multiple that two or more numbers have in common. It is a crucial concept in mathematics that is used in various fields, including physics, engineering, and computer science.

Understanding LCM

To understand how to find the LCM of two numbers, we need to understand what multiples are. A multiple is a result of multiplying a number by an integer. For instance, the multiples of 7 are 7, 14, 21, 28, 35, and so on. The multiples of 8 are 8, 16, 24, 32, 40, and so on.

What is the LCM of 7 and 8?

To find the LCM of 7 and 8, we need to list their multiples and identify the smallest common multiple. The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and so on. From this, we can see that the smallest common multiple of 7 and 8 is 56.

How to Find LCM using Prime Factorization

Another method of finding the LCM of two or more numbers is by using prime factorization. Prime factorization is the process of finding the prime numbers that can multiply to give a particular number. For instance, the prime factors of 12 are 2 and 3. To find the LCM of 7 and 8 using prime factorization, we need to follow these steps:
  1. Find the prime factors of each number. The prime factors of 7 are 7, and those of 8 are 2 and 2.
  2. Multiply the highest power of each prime factor. In this case, the highest power of 2 is 3 (2 x 2 x 2 = 8), and the highest power of 7 is 1 (7).
  3. Multiply the results from step two. Therefore, the LCM of 7 and 8 is 56 (2 x 2 x 2 x 7 = 56).

Applications of LCM

LCM is used in various fields, including:
  1. In physics, LCM is used to calculate the time it takes two objects to meet or collide.
  2. In computer science, LCM is used in scheduling tasks and managing resources.
  3. In engineering, LCM is used in designing machines and systems by determining the time it takes for different components to complete a cycle.

Conclusion

In conclusion, LCM is an essential concept in mathematics that is used in various applications. It is the smallest multiple that two or more numbers have in common, and it can be found using different methods, including listing multiples and using prime factorization.

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