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LCM

# How To Find LCM of 48 and 56? | Listing, Division, and Prime Factorization Method

Written by Prerit Jain

Updated on: 17 Feb 2023

### How To Find LCM of 48 and 56? | Listing, Division, and Prime Factorization Method

LCM of 48 and 56 is 336. LCM of 48 and 56, also known as the Least Common Multiple or Lowest Common Multiple of 48 and 56 is the lowest possible common number that is divisible by 48 and 56.

Now, let’s see how to find the LCM of 48 and 56. Multiples of 48 are 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576, 624, 672, 720, 768,… and multiples of 56 are 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784,… Here, both 336 and 672 are the common multiples in the multiples of 48 and 56, respectively, or that are divisible by 48 and 56. But, when you have to find the LCM, you must focus on the lowest common number. So, 336 is the lowest common number among all the multiples that is divisible by 48 and 56, and hence the LCM of 48 and 56 is 336.

## Methods to Find the LCM of 48 and 56

There are three different methods for finding the LCM of 48 and 56. These methods are:

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

## LCM of 48 and 56 using the Prime Factorization Method

The prime factorization method is one of the methods for finding the LCM. To find the LCM of 48 and 56 using the prime factorization method, follow the following steps:

• Step 1: Find the prime factors of 48 and 56 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 48 and 56.

LCM of 48 and 56 can be obtained using the prime factorization method as

• Prime factorization of 48 can be expressed as 2 * 2 * 2 * 2 * 3 = 21 * 21 * 2* 21 * 31 = 24 * 31
• Prime factorization of 56 can be expressed as 2 * 2 * 2 * 2 * 3 * 7 = 21 * 21 * 2* 21 * 3* 71 = 24 * 3* 7

So, the LCM of 48 and 56 = 24 * 31 * 71 = 2 * 2 * 2 * 2 * 3 * 7 = 336

## LCM of 48 and 56 Using the Listing Method

The listing method is one of the methods for finding the LCM. To find the LCM of 48 and 56 using the listing method, follow the following steps:

• Step 1: Write down the first few multiples of 48 and 56 separately.
• Step 2: Out of all the multiples of 48 and 56 focus on the multiples that are common to both the numbers, that is, 48 and 56.
• Step 3: Now, out of all the common multiples, take out the smallest common multiple. That will be the LCM of 48 and 56.

LCM of 48 and 56 can be obtained using the listing method as

• Multiples of 48 are 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576, 624, 672, 720, 768,…
• Multiples of 56 are 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784,…

Here, it is clear that the least common multiple is 336. So, the LCM of 48 and 56 is 336.

## LCM of 48 and 56 Using the Division Method

The division method is one of the methods for finding the LCM of any two or more numbers. To find the LCM of 48 and 56 using the division method, divide 48 and 56 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 48 and 56.

Follow the following steps to find the LCM of 48 and 56 using the division method:

• Step 1: Write the numbers for which you have to find the LCM, that is 48 and 56 in this case, separated by commas.
• Step 2: Now, find the smallest prime number which is divisible by either 48 or 56.
• Step 3: If any of the numbers between 48 and 56 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 48 and 56.

LCM of 48 and 56 can be obtained using the division method:

So, the LCM of 48 and 56 = 2 * 2 * 2 * 2 * 3 * 7 = 336

## What Is the Formula for Finding the LCM of 48 and 56?

LCM of 48 and 56 can be calculated using the formulas given below:

LCM (48, 56) = (48 * 56) / HCF (48, 56),
where HCF is the highest common factor or the greatest common divisor of 48 and 56.

Another formula, using which the LCM of 48 and 56 can be found:
48 * 56 = LCM (48, 56) * HCF (48, 56), that is,
the product of 48 and 56 is equal to the product of its LCM and HCF.

## Problems Based on LCM of 48 and 56

Question 1: What is the least perfect square divisible by 48 and 56?
Solution:
The least number divisible by 48 and 56 is the LCM of 48 and 56, that is, 336.
Using prime factorization, we can expand and write the LCM of 48 and 56 as 2 * 2 * 2 * 2 * 3 * 2 * 2 * 2 * 2 * 3 * 7.
Here, we didn’t get complete pairs for all numbers, so to make the pairs complete, we will multiply 7 by all the numbers.
Hence, the least perfect square divisible by 48 and 56 is:
LCM(48, 56) * 7 = 2 * 2 * 2 * 2 * 3 * 2 * 2 * 2 * 2 * 3 * 7 * 7= 112896

Question 2: Find the LCM of 48 and 56 using the listing method.
Solution:

To find the LCM of 48 and 56 using the listing method, first, we will write down the first few multiples of 48 and 56 separately. Out of all the multiples of 48 and 56, we will focus on the multiples which are common to both numbers.
Then, out of all the common multiples, we will take out the smallest common multiple. That will be the LCM of 48 and 56.

• Multiples of 48 are 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576, 624, 672, 720, 768,…
• Multiples of 56 are 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784,…

Here, it is clear that the least common multiple is 336. So, the LCM of 48 and 56 is 336.

Question 3: What is the LCM of 24, 48, and 56?
Solution:

We will find the LCM of 24, 48, and 56 using the division method:
To find the LCM of 24, 48, and 56 using the division method, first, we will find the smallest prime number which is divisible by either 24 or 48, or 56. If any of the numbers among 24, 48, and 56 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 24, 48, and 56.

So, the LCM of 48 and 56 = 2 * 2 * 2 * 2 * 3 * 7 = 336

Question 4: Find the LCM of 48 and 56 using the prime factorization method.
Solution:

To find the LCM of 48 and 56 using the prime factorization method, first, we will find the prime factors of 48 and 56 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 48 and 56.

• Prime factorization of 48 can be expressed as 2 * 2 * 2 * 2 * 3 = 21 * 21 * 2* 21 * 31 = 24 * 31
• Prime factorization of 56 can be expressed as 2 * 2 * 2 * 2 * 3 * 7 = 21 * 21 * 2* 21 * 3* 71 = 24 * 3* 7

So, the LCM of 48 and 56 = 24 * 31 * 71 = 2 * 2 * 2 * 2 * 3 * 7 = 336

Question 5: If the product of two numbers is 2688 and their HCF is 8, find the LCM.
Solution:

As we know, product of two numbers = LCM * HCF
It is given that, product of the numbers = 2688 and HCF = 8
So, 2688 = LCM * 8
LCM = 2688 / 8
LCM = 336
Hence, the LCM is 336.

What is the LCM of 48 and 56?
LCM of 48 and 56 is 336.

Are the LCM of 48 and 56 the same as the LCM of 24, 48, and 56?
LCM of 48 and 56 is 336 and LCM of 24, 48, and 56 is also 336. So, the LCM of 48 and 56 are the same as the LCM of 24, 48, and 56.

What are the methods to find the LCM of 48 and 56?
There are 3 major methods for finding the LCM of 48 and 56. These methods are:

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

Is 672 also considered as the LCM of 48 and 56?
No, 672 is not considered as the LCM of 48 and 56. 672 is a common multiple of 48 and 56. But, it is not the least common number which is divisible by 48 and 56, and while finding the LCM, you must focus on the lowest common number. So, 336 is the lowest common number divisible by 48 and 56.

Are LCM and HCF of 48 and 56 the same?
LCM of 48 and 56 is 336 and HCF of 48 and 56 is 8. So, LCM and HCF of 48 and 56 are not the same.

We hope you understand all the basics of how to find the LCM of 48 and 56.

Written by by

Prerit Jain

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