Understanding The Lcm Of 2 And 9

Ex 3.7, 10 Find the LCM of the following numbers Class 6 Teachoo from www.teachoo.com

What is LCM?

LCM stands for Least Common Multiple. It is the smallest positive integer that is divisible by two or more given numbers without leaving any remainder. In other words, it is the smallest number that is a multiple of all the given numbers.

How to Find the LCM?

To find the LCM of two or more numbers, there are several methods that can be used. One method is to list the multiples of each number until you find the smallest multiple that is common to all of them. Another method is to use prime factorization, where you find the prime factors of each number and multiply the highest power of each factor together.

The LCM of 2 and 9

To find the LCM of 2 and 9, we can use either of the methods mentioned above. Let's start with the listing method. The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40... and so on. The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90... and so on. From these lists, we can see that the smallest common multiple of 2 and 9 is 18.

Why is 18 the LCM?

We can check that 18 is indeed the LCM of 2 and 9 by verifying that it is divisible by both 2 and 9. 18 divided by 2 is 9, which is a whole number with no remainder. 18 divided by 9 is 2, which is also a whole number with no remainder. Therefore, 18 is the smallest positive integer that is divisible by both 2 and 9.

Applications of LCM

LCM has many practical applications in mathematics and real life. For example, it can be used to find the time when two events, such as trains or buses, will occur at the same time. It can also be used to simplify fractions and solve algebraic equations. Additionally, LCM is used in computer science to determine the optimal size of memory buffers and other computer algorithms.

Conclusion

In conclusion, the LCM of 2 and 9 is 18. LCM is a useful concept in mathematics and has many applications in real life. By understanding LCM and how to find it, we can solve a variety of problems in different fields.