Understanding The Lcm Of 15 And 6

LCM of 6 and 15 How to Find LCM of 6, 15? from www.cuemath.com

Introduction

In mathematics, we often come across situations where we need to find the lowest common multiple (LCM) of two or more numbers. The LCM is the smallest multiple that two or more numbers have in common. In this article, we will focus on finding the LCM of 15 and 6.

What is LCM?

LCM stands for the lowest common multiple. It is the smallest number that is a multiple of two or more given numbers. In other words, it is the smallest number that can be divided by each of the given numbers without a remainder.

What is 15?

15 is a natural number that comes after 14 and before 16. It is an odd number and is divisible by 3 and 5. It is also known as a composite number, which means it has more than two factors.

What is 6?

6 is a natural number that comes after 5 and before 7. It is an even number and is divisible by 2 and 3. Like 15, it is also a composite number.

How to Find the LCM of 15 and 6?

There are various methods to find the LCM of two numbers. One of the commonly used methods is the prime factorization method. In this method, we will express both 15 and 6 as a product of their prime factors. 15 can be expressed as 3 x 5, and 6 can be expressed as 2 x 3. Now, we need to take all the prime factors and their highest powers that occur in either of the two factorizations. In this case, we have 2, 3, and 5. The highest power of 2 is 2^1, the highest power of 3 is 3^1, and the highest power of 5 is 5^1. Multiplying these powers, we get 2 x 3 x 5 = 30. Therefore, the LCM of 15 and 6 is 30.

Why is 30 the LCM of 15 and 6?

To understand why 30 is the LCM of 15 and 6, we need to consider the multiples of both 15 and 6. The multiples of 15 are 15, 30, 45, 60, 75, 90, and so on. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, and so on. From the above multiples, we can see that the smallest number that is common to both 15 and 6 is 30. Hence, 30 is the LCM of 15 and 6.

Conclusion

In conclusion, the LCM of 15 and 6 is 30. To find the LCM of two numbers, we can use various methods such as prime factorization, listing multiples, or using a Venn diagram. The LCM is an important concept in mathematics and is used in various areas such as fractions, ratios, and proportions.