Understanding The Least Common Multiple (Lcm) Of 3 And 4

Write All the Numbers Less Than 100 Which Are Common Multiples of 3 and from www.cuemath.com

Introduction

As a professional teacher, I understand that mathematics can be challenging for some students, especially when it comes to finding the least common multiple (LCM). In this article, we will discuss the LCM of 3 and 4 and provide solutions on how to find it.

What is LCM?

LCM is the smallest multiple that is common to two or more numbers. In simple terms, it is the smallest number that is a multiple of two or more numbers. For example, the LCM of 2 and 3 is 6 because 6 is the smallest number that both 2 and 3 can divide into.

How to Find the LCM of 3 and 4?

There are different methods to find the LCM of 3 and 4. One common method is to list the multiples of both numbers and find the smallest common multiple. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, and so on. From the list, we can see that the smallest common multiple of 3 and 4 is 12.

The Prime Factorization Method

Another method to find the LCM of 3 and 4 is the prime factorization method. To use this method, we need to find the prime factors of the numbers and multiply them together. The prime factors of 3 are 3, while the prime factors of 4 are 2 and 2. We can write 3 as 3^1 and 4 as 2^2. To find the LCM, we take the highest power of each prime factor, which is 3^1 and 2^2. We multiply them together to get 12, which is the LCM of 3 and 4.

The Formula Method

The formula method is another way to find the LCM of 3 and 4. The formula for finding the LCM of two numbers is LCM(a, b) = (a x b) / GCD(a, b), where GCD is the greatest common divisor. The GCD of 3 and 4 is 1, so we can substitute the values in the formula to get LCM(3, 4) = (3 x 4) / 1 = 12.

Conclusion

In conclusion, the LCM of 3 and 4 is 12. We can find it through different methods such as listing the multiples, prime factorization, and using the formula. As a teacher, it is important to explain these methods to students to help them understand and solve mathematical problems with ease.