# What is the Least Common Multiple of 7 and 6?

If you’re wondering what the least common multiple of 7 and 6 is, you’re in the right place! In this article, we’ll guide you through the process of finding the LCM step by step.

## Introduction

If you have never heard of the least common multiple (LCM) before, don’t worry. It’s a relatively simple concept that is used in many areas of math, including algebra and geometry. The LCM is the smallest positive integer that is a multiple of two or more integers. In this article, we will explore how to find the LCM of 7 and 6.

## Understanding Factors of 7 and 6

Before we can find the LCM of 7 and 6, we need to understand the factors of each number. A factor is a number that divides into another number without leaving a remainder.

### Identifying Prime Factors of 7

The number 7 is a prime number, which means it is only divisible by 1 and itself. Therefore, the only factors of 7 are 1 and 7.

### Identifying Prime Factors of 6

The number 6 is not a prime number because it is divisible by numbers other than 1 and itself. The prime factors of 6 are 2 and 3. This means that 6 can be expressed as the product of 2 and 3, or 2 * 3.

Now that we know the prime factors of 7 and 6, we can move on to finding the common factors between them.

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## Finding Common Factors

To find the common factors of 7 and 6, we need to list all the factors of each number and identify which ones they have in common.

### Listing Factors of 7 and 6

The factors of 7 are 1 and 7, while the factors of 6 are 1, 2, 3, and 6.

### Identifying Common Factors

The only factor that 7 and 6 have in common is 1. Therefore, 1 is the only common factor between them.

## Finding Least Common Multiple

Now that we have identified the common factor between 7 and 6, we can find the LCM by multiplying the common factor by the product of the remaining factors.

### Multiplying Common Factors

The common factor between 7 and 6 is 1. The product of the remaining factors is 2 3 7, which is equal to 42.

### Identifying the Smallest Multiple

To find the LCM, we need to divide the product of the remaining factors by the common factor. This gives us:

LCM = (2 3 7) / 1 = 42

Therefore, the LCM of 7 and 6 is 42.

Now that we have found the LCM of 7 and 6, we can check our answer to ensure that it is correct.

## Finding Least Common Multiple

To find the LCM of 7 and 6, we need to identify the common factors and the smallest multiple that includes all of them.

### Multiplying Common Factors

The common factors of 7 and 6 are 1 and 2. To find the LCM, we multiply the common factors together.

1 * 2 = 2

Therefore, the LCM of 7 and 6 is 2.

### Identifying the Smallest Multiple

We can also find the LCM of 7 and 6 by listing out the multiples of each number until we find the smallest multiple that they share.

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Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

From the lists above, we can see that the smallest multiple that both 7 and 6 share is 42. Therefore, the LCM of 7 and 6 is 42.

Now that we have found the LCM of 7 and 6, it’s important to check our answer to make sure it’s correct. There are two methods we can use to verify the LCM.

### Verification Using Multiplication

We can verify the LCM by multiplying the two original numbers (7 and 6) and dividing by their greatest common factor (GCF).

The GCF of 7 and 6 is 1, so:

(7 * 6) / 1 = 42

Our answer of 42 matches the LCM we found earlier, so we know that it is correct.

### Verification Using Division

We can also verify the LCM by dividing the LCM by each of the original numbers and making sure there is no remainder.

42 / 7 = 6 with no remainder
42 / 6 = 7 with no remainder

Since there is no remainder when we divide the LCM by each of the original numbers, we know that 42 is indeed the LCM of 7 and 6.

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