Understanding The Least Common Multiple (Lcm) Of 5 And 7

LCM of 5 and 7 How to Find LCM of 5, 7? from www.cuemath.com

Introduction

As a student of mathematics, it is crucial to understand the concept of Least Common Multiple (LCM) and its application in solving mathematical problems. The LCM is a fundamental concept in arithmetic and plays a vital role in various fields like engineering, computer science, economics, and many more.

Definition of LCM

The LCM is the smallest positive integer that is divisible by two or more given integers without leaving any remainder. In simpler terms, it is the lowest common multiple of two or more numbers.

Calculating the LCM of 5 and 7

To calculate the LCM of two numbers, you can use different methods like prime factorization, listing multiples, or using the formula. In this article, we will use the prime factorization method to find the LCM of 5 and 7.

Prime Factorization Method

The prime factorization of a number is the unique representation of that number as a product of its prime factors. To find the LCM of 5 and 7, we need to factorize both numbers.

5 is a prime number, and its prime factorization is 5.

7 is also a prime number, and its prime factorization is 7.

Multiplying Prime Factors

To find the LCM, we need to multiply the prime factors of both numbers. In this case, we only have one prime factor for each number, so we multiply them as follows:

LCM of 5 and 7 = 5 x 7 = 35

Therefore, the LCM of 5 and 7 is 35. This means that 35 is the smallest positive integer that is divisible by both 5 and 7 without leaving any remainder.

Conclusion

In conclusion, the LCM is a vital concept in mathematics that helps in solving various real-life problems. In this article, we have explained the definition of LCM and how to calculate the LCM of two numbers using the prime factorization method. By understanding the LCM, you can solve more complex problems that involve multiple numbers.