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LCM

# How to Find the LCM of 9 and 15? | Listing, Division, and Prime Factorization Method

Written by Prerit Jain

Updated on: 15 Feb 2023

### How to Find the LCM of 9 and 15? | Listing, Division, and Prime Factorization Method

LCM of 9 and 15 is 45. LCM of 9 and 15, also known as Least Common Multiple or Lowest Common Multiple of 9 and 15, is the lowest possible common number that is divisible by 9 and 15.

Let’s have a look at how to find the LCM of 9 and 15. So, multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99,… and multiples of 15 are 15, 30, 45, 60, 75, 90, 105,… Here, both 45 and 90 are the common numbers that are divisible by the given numbers, that is, 9 and 15. But, when you have to find the LCM, you must focus on the lowest common number. So, 45 is the lowest common number divisible by 9 and 15, and hence the LCM of 9 and 15 is 45.

The detailed steps on how to find the LCM of 9 and 15 using the Listing method, Prime Factorization method, and Division method are explained on this page. Scroll down to find out more.

## Methods to find the LCM of 9 and 15

There are three major methods, using which you can find the LCM of 6 and 15:

• Listing Method
• Division Method
• Prime Factorization Method

## LCM of 9 and 15 using the Listing Method

The listing method is one of the methods for finding the LCM. If you want to find the LCM of 9 and 15 using the listing method, you can go through the following steps:

• Step 1: Write down the first few multiples of 9 and 15 separately.
• Step 2: Out of all the multiples of 9 and 15 focus on the multiples that are common to both the numbers, that is, 9 and 15.
• Step 3: Now, out of all the common multiples, take out the smallest common multiple. That will be the LCM of 9 and 15.

Finding the LCM of 9 and 15 using the listing method:

• Step 1: Multiples of 9 are 9, 18, 27, 36, 45, 54, 63,…
• Step 2: Multiples of 15 are 15, 30, 45, 60, 75, 90, 105,…
• Step 3: Here, it is clear that the least common multiple is 45. So, the LCM of 9 and 15 is 45.

## LCM of 9 and 15 Using the Division Method

The division method is one of the methods for finding the LCM. If you want to find the LCM of 9 and 15 using the division method, divide 9 and 15 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 9 and 15.

You can go through the following steps to find the LCM of 9 and 15 using the division method:

• Step 1: Write the numbers for which you have to find the LCM, that is 9 and 15 in this case, separated by commas.
• Step 2: Now, find the smallest prime number which is divisible by either 9 or 15.
• Step 3: If any of the numbers among 9 and 15 is not divisible by the respective prime number, write that number in the next row just below it and proceed further.
• Step 4: Continue dividing the numbers obtained after each step by the prime numbers, until you get the result as 1 in the entire row.
• Step 5: Now, multiply all the prime numbers and the final result will be the LCM of 9 and 15.

LCM of 9 and 15 can be found using the division method:

So, LCM of 9 and 15 = 3 * 3 * 5 = 45

## LCM of 9 and 15 Using the Prime Factorization Method

The prime factorization method is one of the methods for finding the LCM. If you want to find the LCM of 9 and 15 using the prime factorization method, you can go through the following steps:

• Step 1: Find the prime factors of 9 and 15 using the repeated division method.
• Step 2: Write all the prime factors of 9 and 15 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 9 and 15.

LCM of 9 and 15 can be found using the prime factorization method as:

• Step 1: Prime factorization of 9 can be expressed as 3 * 3 = 31 * 31 = 32
• Step 2: Prime factorization of 15 can be expressed as 3 * 5 = 31 * 51
• Step 3: So, the LCM of 9 and 15 = 32 * 51 = 3 * 3 * 5 = 45

## What Is the Formula to Find the Lcm of 9 and 15?

LCM of 9 and 15 can be calculated using the formula:

LCM (9, 15) = (9 * 15) / HCF (9, 15),
where HCF is the highest common factor or the greatest common divisor of 9 and 15.

Another formula for finding the LCM of 9 and 15 is:

9 * 15 = LCM (9, 15) * HCF (9, 15), that is,
the product of 9 and 15 is equal to the product of its LCM and HCF.

## Problems Based on LCM of 9 and 15

Question 1: What is the least possible number which is divisible by 9 and 15?
Solution:
There are three methods by which you can find the least possible number which is divisible by 9 and 15.
Here, we will find it by using the listing method:

• Step 1: First, we will write down the first few multiples of 9 and 15 separately. Then, out of all the multiples of 9 and 15, we will focus on the multiples which are common to both the numbers, that is, 9 and 15.
• Step 2: Now, out of all the common multiples, we will take out the smallest common multiple. The final result after multiplication will be the least possible number, which is divisible by both 9 and 15.
• Step 3: Multiples of 9 are 9, 18, 27, 36, 45, 54, 63,…Multiples of 15 are 15, 30, 45, 60, 75, 90, 105,…
• Step 4: Here, the least common multiple is 45. So, the least possible number, which is divisible by 6 and 9 is 45.

Question 2: What is the LCM of 5, 9, and 15?
Solution:
We will find the LCM of 5, 9, and 15 using the division method:

So, the LCM of 5, 9, and 15 = 3 * 3 * 5 = 45

Question 4: Find the LCM of 9 and 15 using the prime factorization method.
Solution:
Let’s find the LCM of 9 and 15 using the prime factorization method:

• Step 1: First, we will find the prime factors of 9 and 15 using the repeated division method.
• Step 2: Then, we will write all the prime factors in their exponent forms and multiply the prime factors having the highest power.
• Step 3: The final result after multiplication will be the LCM of 9 and 15.
• Step 4: Prime factorization of 9 can be expressed as 3 * 3 = 31 * 31 = 32
• Step 5: Prime factorization of 15 can be expressed as 3 * 5 = 31 * 51. So, the LCM of 9 and 15 = 32 * 51 = 3 * 3 * 5 = 45

Question 5: Find the LCM of 5 and 15 using the listing method.
Solution:
Let’s find the LCM of 5 and 15 using the listing method:

• Step 1: First, we will write down the first few multiples of 5 and 15 separately. Out of all the multiples of 5 and 15, we will focus on the multiples which are common to both.
• Step 2: Then, out of all the common multiples, we will take out the smallest common multiple. That will be the LCM of 5 and 15.
• Step 3: Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45,…Multiples of 15 are 15, 30, 45, 60, 75, 90, 105,…
• Step 4: Here, the least common multiple is 45. So, the LCM of 5 and 15 is 45.

Are LCM and HCF of 9 and 15 the same?
LCM of 9 and 15 is 45 and HCF of 9 and 15 is 3. So, LCM and HCF of 9 and 15 are not the same.

What are the ways using which you can find the 9 and 15?
There are 3 major ways using which you can find the LCM of 9 and 15:

Is 90 also considered as the LCM of 9 and 15?
No, 90 is not considered as the LCM of 9 and 15. 90 is a common number that is divisible by 9 and 15. But, it is not the least common number which is divisible by 9 and 15 and when you have the find the LCM, you must focus on the lowest common number. So, 45 is the lowest common number divisible by 9 and 15.

Are the LCM of 9 and 15 the same as the LCM of 5, 9, and 15?
LCM of 9 and 15 is 45 and LCM of 5, 9, and 15 is 45. So, the LCM of 9 and 15 are the same as the LCM of 5, 9, and 15.

What is the LCM of 9 and 15?
LCM of 9 and 15 is 45.

We hope you understand all the basics on how to find the LCM of 9 and 15.

Written by by

Prerit Jain

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