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.

Checking the Answer

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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