LCM

# How To Find LCM of 6 and 9? | Listing, Division, and Prime Factorization Method

Written by Prerit Jain

Updated on: 18 Feb 2023

Contents

### How To Find LCM of 6 and 9? | Listing, Division, and Prime Factorization Method

The LCM of 6, and 9 is 18. The **Least Common Multiple**, or Lowest Common Multiple, is the lowest possible common number that is divisible by given numbers.

Let’s take the examples of 6 and 9. **Multiples of 6** are 6, 12, 18, 24, 30, 36, and **multiples of 9** are 9, 18, 27, 36, Here, both 18 and 36 are the common numbers that are divisible by the given numbers, that is, 6 and 9. But, when you have found the LCM, you must take the lowest common number. So, 18 is the lowest common number divisible by 6 and 9, and hence the LCM of 6 and 9 is 18.

The detailed steps on how to find the LCM of 6 and 9 using the Listing method, Prime Factorization method, and Division method are explained on this page. Scroll down to find out more.

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## How to Find the LCM of 6 and 9?

The LCM of 6 and 9 is 18. The three method to find least common multiple of 6 and 9 are explained below:

- Division Method
- Prime Factorization Method
- Listing Method

## LCM of 6 and 9 using the Division Method

To find the LCM of 6 and 9 using the division method, divide 6 and 9 by the smallest prime number that is either divisible by 6 or 9. Then, using the prime factors from the division method of 6 and 9, we can find the LCM of 6 and 9.

You can follow the following steps to find the LCM of 6 and 9 using the division method:

- Step 1: Write the numbers for which you have to find the LCM, that is, 6 and 9, separated by commas.
- Step 2: Locate the smallest prime number that can be divided by 6 or 9. The smallest prime number that is divisible by 6 is 2; the smallest prime number that is divisible by 9 is 3.
- Step 3: Because number 2 is divisible by 6 but not by 9, we’ll keep 9 until we find the smallest prime number that is divisible by 9. Hence, we will be writing the number 9 in the next row just below it and dividing the number 6 by the smallest prime number.
- Step 4: Dividing the number 6 by 2, gives us 3. The number 9 is not divisible by 2, hence we are keeping it as it is and adding 3 under the first number column.
- Step 5: Now the smallest prime number that divides 3 and 9 is 3. Hence, we will divide the number 3 and 9 with the smallest prime number until we get 1, as shown in the table below.
- Step 6: Now, multiply all the prime numbers and the final result will be the LCM of 6 and 9.

LCM of 6 and 9 can be found using the division method:

Prime Factors | First Number | Second Number |

2 | 6 | 9 |

3 | 3 | 9 |

3 | 1 | 3 |

1 | 1 |

So, LCM of 6 and 9 = 2 * 3 * 3 = 18

## How To Find LCM of 6 and 9 using the Prime Factorization Method?

To find the LCM of 6 and 9 using the prime factorization method, you can follow the following steps:

- Step 1: Find the prime factors of 6 and 9 using the repeated division method.
- Step 2: Write all the prime factors in their exponent forms. Then multiply the prime factors having the highest power.
- Step 3: The final result after multiplication will be the LCM of 6 and 9.

LCM of 6 and 9 can be found using the prime factorization method as:

Prime factorization of 6 can be expressed as 2 * 3 = 2^{1} * 3^{1}

Prime factorization of 9 can be expressed as 3 * 3 = 3^{1} * 3^{1} = 3^{2}

So, the LCM of 6 and 9 = 2^{1} * 3^{2 }= 2 * 3 * 3 = 18

## How To Find LCM of 6 and 9 using the Listing Method?

To find the LCM of 6 and 9 using the listing method, you can follow the following steps:

- Step 1: Write down the first few multiples of 6 and 9 separately.
- Step 2: Out of all the multiples of 6 and 9 focus on the multiples which are common to both, 6 and 9.
- Step 3: Now, out of all the common multiples, take out the smallest common multiple. That will be the LCM of 6 and 9.

LCM of 6 and 9 can be found using the listing method as:

- Multiples of 6 are 6, 12, 18, 24, 30, 36, 42,…
- Multiples of 9 are 9, 18, 27, 36, 45, 54, 63,…

Here, it is clear that the least common multiple is 18.

So, the LCM of 6 and 9 is 18.

## What is The Formula for Finding the LCM of 6 and 9?

LCM of 6 and 9 can be calculated using the formula:

LCM (6, 9) = (6 * 9) / HCF (6, 9),

where, HCF is the highest common factor or the greatest common divisor of 6 and 9.

Another formula for finding the LCM of 6 and 9 is:

6 * 9 = LCM (6, 9) * HCF (6, 9), that is,

The product of 6 and 9 is equal to the product of its LCM and HCF.

## Problems Based on LCM of 6 and 9

**Question 1: If the product of two numbers is 54, their LCM is 18, HCF is 3, and one of the numbers is 9, find the other number.Solution:**

As we know,

Product of two numbers = LCM * HCF

It is given that,

One of the numbers = 9, LCM = 18, and HCF = 3

Let the other number be x.

So, 9 * x = 18 * 3

x = (18 * 3) / 9

x = 54 / 9

x = 6

Hence, the other number is 6.

**Question 2: What is the least possible number which is divisible by 6 and 9?Solution: **

There are three methods using which you can find the least possible number which is divisible by 6 and 9.

We will find it using the prime factorization method. First, we will find the prime factors of 6 and 9 using the repeated division method. Then, we will write all the prime factors in their exponent forms and multiply the prime factors having the highest power.

After that, the final result after multiplication will be the least possible number which is divisible by 6 and 9.

Prime factorization of 6 can be expressed as 2 * 3 = 2

^{1}* 3

^{1}

Prime factorization of 9 can be expressed as 3 * 3 = 3

^{1}* 3

^{1}= 3

^{2}

So, the least possible number which is divisible by 6 and 9 is 2

^{1}* 3

^{2 }= 2 * 3 * 3 = 18.

**Question 3: Find the LCM of 2 and 9 using the listing method.Solution: **

To find the LCM of 2 and 9 using the listing method, first, we will write down the first few multiples of 2 and 9 separately. Out of all the multiples of 2 and 9, we will focus on the multiples which are common to both.

Then, out of all the common multiples, we will take out the smallest common multiple. That will be the LCM of 2 and 9.

Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18,…

Multiples of 9 are 9, 18, 27, 36, 45, 54, 63,…

Here, the least common multiple is 18.

So, the LCM of 2 and 9 is 18.

**Question 4: Find the LCM of 6 and 9 using the division method.Solution: **

To find the LCM of 6 and 9 using the division method, first, we will divide 6 and 9 by the smallest prime number, which is divisible by any of them. Then, the prime factors further obtained will be used to calculate the final LCM of 6 and 9.

Prime Factors | First Number | Second Number |

2 | 6 | 9 |

3 | 3 | 9 |

3 | 1 | 3 |

1 | 1 |

So, LCM of 6 and 9 = 2 * 3 * 3 = 18

**Question 5: What is the LCM of 2, 6, and 9?Solution: **

We will find the LCM of 2, 6, and 9 using the listing method:

Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18,…

Multiples of 6 are 6, 12, 18, 24, 30, 36,…

Multiples of 9 are 9, 18, 27, 36, 45, 54, 63,…

Here, the least common multiple is 18.

So, the LCM of 3, 6, and 9 is 18.

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## FAQs on LCM of 6 and 9

**What is the LCM of 6 and 9?**

LCM of 6 and 9 is 18.

**Are LCM and HCF of 6 and 9 the same?**

LCM of 6 and 9 is 18 and HCF of 6 and 9 is 3. So, LCM and HCF of 6 and 9 are not the same.

**What are the ways using which you can find the 6 and 9?**

There are 3 major ways using which you can find the LCM of 6 and 9:

1. Division Method

2. Listing Method

3. Prime Factorization Method

**Is the LCM of 6 and 9 the same as the LCM of 2, 3, and 9?**

LCM of 6 and 9 is 18 and LCM of 2, 3, and 9 is 18. So, the LCM of 6 and 9 are the same as the LCM of 2, 3, and 9.

**Is 36 also considered as the LCM of 6 and 9?**

36 isn’t considered as the LCM of 6 and 9. 36 is a common number that is divisible by 6 and 9. But, it is not the least common number which is divisible by 6 and 9 and when you have the find the LCM, you must take the lowest common number. So, 18 is the lowest common number divisible by 6 and 9.

We hope you understand all the basics on how to find the LCM of 6 and 9.

Written by

Prerit Jain