The Least Common Multiple Of 7 And 5

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

Introduction

As a teacher, one of the most important and exciting things is to teach students about numbers, especially when it comes to finding the least common multiple (LCM) of two or more numbers. In this article, we will explore the concept of LCM, specifically for the numbers 7 and 5. We will discuss what LCM is, how to find it, and provide an explanation of the LCM of 7 and 5.

What is LCM?

The Least Common Multiple, or LCM, is the smallest positive integer that is divisible by two or more numbers. In other words, it is the smallest number that is a multiple of two or more given numbers. For example, the LCM of 2 and 3 is 6 because 6 is the smallest number that is divisible by both 2 and 3.

Finding the LCM of 7 and 5

To find the LCM of 7 and 5, we need to list down the multiples of each number until we find a common multiple. A multiple of a number is the result of multiplying it by a positive integer. For example, the multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, and so on. Similarly, the multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, and so on. We can see that the first common multiple of 7 and 5 is 35, which is the smallest multiple that is common to both lists. Therefore, the LCM of 7 and 5 is 35.

Explanation of the LCM of 7 and 5

The LCM of 7 and 5 is 35 because it is the smallest positive integer that is divisible by both 7 and 5. We can see that 35 is a multiple of 7 because 7 multiplied by 5 is equal to 35. Similarly, we can see that 35 is also a multiple of 5 because 5 multiplied by 7 is equal to 35. Therefore, 35 is the smallest number that is a multiple of both 7 and 5. It is important to note that there can be multiple LCMs for any given set of numbers, but the LCM we found is the least or smallest one.

Why is LCM important?

LCM is an important concept in mathematics because it helps us to find various solutions to real-world problems. For example, if we want to plan a picnic with 7 friends and we want to buy enough food for everyone, we need to know the LCM of 7 to determine how many sandwiches we should buy. Similarly, if we want to distribute 5 books equally among 7 students, we need to know the LCM of 5 to determine how many books each student will receive.

Conclusion

In conclusion, the LCM of 7 and 5 is 35, which is the smallest number that is divisible by both 7 and 5. LCM is an important concept in mathematics that helps us to solve various real-world problems. By understanding how LCM works, we can apply it to many different situations and find solutions efficiently.