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LCM

# How to Find the LCM of 120 and144? | Listing, Division, and Prime Factorization Method

Written by Prerit Jain

Updated on: 17 Feb 2023

### How to Find the LCM of 120 and144? | Listing, Division, and Prime Factorization Method

LCM of 120 and 144 is 720. LCM of 120 and 144, also known as the Least Common Multiple or Lowest Common Multiple of 120 and 144 is the lowest possible common number that is divisible by 120 and 144.

Now, let’s see how to find the LCM of 120 and 144. Multiples of 120 are 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560,… and multiples of 144 are 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440, 1584, 1728, 1872,… Here, both 720 and 1440 are the common numbers in the multiples of 120 and 144, respectively, or that are divisible by 120 and 144. But, when you have to find the LCM, you must focus on the lowest common number. So, 720 is the lowest common number among all the multiples that is divisible by 120 and 144, and hence the LCM of 120 and 144 is 720.

## What Are the Methods to Find the LCM of 120 and 144?

There are three different methods for finding the LCM of 120 and 144. They are

1. Listing Method
2. Division Method
3. Prime Factorization Method

## LCM of 120 and 144 Using the Listing Method

The listing method is one of the methods for finding the LCM. To find the LCM of 120 and 144 using the listing method, follow the following steps:

• Step 1: Write down the first few multiples of 120 and 144 separately.
• Step 2: Out of all the multiples of 120 and 144 focus on the multiples that are common to both the numbers, that is, 120 and 144.
• Step 3: Now, out of all the common multiples, take out the smallest common multiple. That will be the LCM of 120 and 144.

LCM of 120 and 144 can be obtained using the listing method as

• Multiples of 120 are 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560,…
• Multiples of 144 are 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440, 1584, 1728, 1872,…

Here, it is clear that the least common multiple is 720. So, the LCM of 120 and 144 is 720.

## LCM of 120 and 144 Using the Division Method

The division method is one of the methods for finding the LCM. To find the LCM of 120 and 144 using the division method, divide 120 and 144 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 120 and 144.

Follow the following steps to find the LCM of 120 and 144 using the division method:

• Step 1: Write the numbers for which you have to find the LCM, that is 120 and 144 in this case, separated by commas.
• Step 2: Now, find the smallest prime number which is divisible by either 120 or 144.
• Step 3: If any of the numbers between 120 and 144 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 120 and 144.

LCM of 120 and 144 can be obtained using the division method as

So, the LCM of 120 and 144 = 2 * 2 * 2 * 2 * 3 * 3 * 5 = 720

## LCM of 120 and 144 Using the Prime Factorization Method

The prime factorization method is one of the methods for finding the LCM. To find the LCM of 120 and 144 using the prime factorization method, follow the following steps:

• Step 1: Find the prime factors of 120 and 144 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 120 and 144.

LCM of 120 and 144 can be obtained using the prime factorization method as

• Prime factorization of 120 can be expressed as 2 * 2 * 2 * 3 * 5 = 21 * 21 * 2* 31 * 51 = 23 * 31 * 51
• Prime factorization of 144 can be expressed as 2 * 2 * 2 * 2 * 3 * 3 = 21 * 21 * 2* 21 * 3* 31 = 24 * 32

So, the LCM of 120 and 144 = 24 * 32 * 51 = 2 * 2 * 2 * 2 * 3 * 3 * 5 = 720

## What Is the Formula for Finding the LCM of 120 and 144

LCM of 120 and 144 can be calculated using the formula:

LCM (120, 144) = (120 * 144) / HCF (120, 144),
where HCF is the highest common factor or the greatest common divisor of 120 and 144.

Another formula, using which the LCM of 120 and 144 can be found:
120 * 144 = LCM (120, 144) * HCF (120, 144), that is,
the product of 120 and 144 is equal to the product of its LCM and HCF.

## Problems Based on LCM of 120 and 144

Question 1: If the product of two numbers is 17280 and their HCF is 24, find the LCM.
Solution:
As we know,
product of two numbers = LCM * HCF
It is given that,
product of the numbers = 17280 and HCF = 24
So, 17280 = LCM * 24
LCM = 17280 / 24
LCM = 720
Hence, the LCM is 720.

Question 2: Find the LCM of 120 and 144 using the prime factorization method.
Solution:

To find the LCM of 120 and 144 using the prime factorization method, first, we will find the prime factors of 120 and 144 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. The final result after multiplication will be the LCM of 120 and 144.

• Prime factorization of 120 can be expressed as 2 * 2 * 2 * 3 * 5 = 21 * 21 * 2* 31 * 51 = 23 * 31 * 51
• Prime factorization of 144 can be expressed as 2 * 2 * 2 * 2 * 3 * 3 = 21 * 21 * 2* 21 * 3* 31 = 24 * 32

So, the LCM of 120 and 144 = 24 * 32 * 51 = 2 * 2 * 2 * 2 * 3 * 3 * 5 = 720

Question 3: What is the least perfect square divisible by 120 and 144?
Solution:

The least number divisible by 120 and 144 is the LCM of 120 and 144, that is, 720.
Using prime factorization, we can expand and write the LCM of 120 and 144 as 2 * 2 * 2 * 3 * 5 * 2 * 2 * 2 * 2 * 3 * 5.
Here, we didn’t get complete pairs for all numbers so to make the pairs complete we will multiply 2 with it.
Hence, the least perfect square divisible by 120 and 144 is
LCM(120, 144) * 2 = 2 * 2 * 2 * 3 * 5 * 2 * 2 * 2 * 2 * 3 * 5 * 2 = 57600

Question 4: What is the LCM of 120, 144, and 360?
Solution:

We will find the LCM of 120, 144, and 360 using the listing method:
To find the LCM of 120, 144, and 360 using the listing method, first, we will write down the first few multiples of 120, 144, and 360 separately. Out of all the multiples of 120, 144, and 360, we will focus on the multiples which are common to all numbers.
Then, out of all the common multiples, we will take out the smallest common multiple. That will be the LCM of 120, 144, and 360.

• Multiples of 120 are 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560,…
• Multiples of 144 are 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440, 1584, 1728, 1872,…
• Multiples of 360 are 360, 720, 1080, 1440, 1800, 2160,…

Here, it is clear that the least common multiple is 720. So, the LCM of 120, 144, and 360 is 720.

Question 5: Find the LCM of 120 and 144 using the division method.
Solution:

To find the LCM of 120 and 144 using the division method, first, we will find the smallest prime number which is divisible by either 120 or 144. If any of the numbers among 120 and 144 is not divisible by the respective prime number, we will write that number in the next row just below it and proceed further. We will continue dividing the numbers obtained after each step by the prime numbers until we get the result as 1 in the entire row. We will multiply all the prime numbers and the final result will be the LCM of 120 and 144.

So, the LCM of 120 and 144 = 2 * 2 * 2 * 2 * 3 * 3 * 5 = 720

Are LCM and HCF of 120 and 144 the same?
LCM of 120 and 144 is 720 and HCF of 120 and 144 is 24. So, LCM and HCF of 120 and 144 are not the same.

What is the LCM of 120 and 144?
LCM of 120 and 144 is 720.

Is 1440 also considered as the LCM of 120 and 144?
No, 1440 is not considered as the LCM of 120 and 144. 1440 is a common multiple of 120 and 144. But, it is not the least common number which is divisible by 120 and 144, and while finding the LCM, you must focus on the lowest common number. So, 720 is the lowest common number divisible by 120 and 144.

Are the LCM of 120 and 144 the same as the LCM of 120, 144, and 360?
LCM of 120 and 144 is 720 and LCM of 120, 144, and 360 is also 720. So, the LCM of 120 and 144 are the same as the LCM of 120, 144, and 360.

What are the methods to find the LCM of 120 and 144?
There are 3 major methods for finding the LCM of 120 and 144:

1. Listing Method
2. Division Method
3. Prime Factorization Method

We hope you understand all the basics of how to find the LCM of 120 and 144.

Written by by

Prerit Jain

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