lcm of 8 and 12

LCM of 8 and 12 is 24. LCM is called Lest Common Multiple. The LCM of two non-zero integers, 8 and 12, is the smallest positive integer 24 which is divisible by both 8 and 12 with no remainder.

In this article, we will learn about what is the LCM of 8 and 12, What is LCM, and How to Find LCM of 8 and 12 using various methods like Prime factorization, Listing Multiples, and By Long Division Method.

What is LCM of 8 and 12?

Answer: LCM of 8 and 12 is 24.

LCM or Least Common Multiple of two numbers means that is the smallest or least number that is multiple of both the numbers for which LCM is calculated.

LCM of 8 and 12 is 24

This means 24 is the smallest possible number which is perfectly divisible by both 8 and 12 leaving without any remainder.

LCM of 8 and 12 Calculator

Try out the following calculator to find the lcm of 8 and 12

How to Find LCM of 8 and 12

Below are various methods used to find LCM of 2 numbers:

• LCM of 8 and 12 by Prime Factorization
• LCM of 8 and 12 by Listing Multiples
• LCM of 8 and 12 by Division

LCM of 8 and 12 by Prime Factorization

Below are the steps for finding LCM of 8 and 12 by prime factorization method:

Step 1: Find the prime factors of the given numbers by repeated division method.

Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power.

Step 3: The product of these factors with the highest powers is the LCM of the given numbers.

The prime factor of 8 and 12, respectively, are,

8 = 2 × 2 × 2 = 2³

12 = 2 × 2 × 3 = 2² × 3

LCM (8, 12) = 2 × 2 × 2 × 3 = 2³ × 3 = 24

LCM of 8 and 12 by Listing Multiples

Below are the steps for finding LCM of 8 and 12 by listing multiples:

Step 1: List the first few multiples of A and B.

Step 2: Mark the common multiples from the multiples of both numbers.

Step 3: Select the smallest common multiple. That lowest common multiple is the LCM of the two numbers.

To calculate the LCM of 8 and 12 by listing out the common multiples, list the multiples as:

Multiples of 8= 8 , 16 , 24 , 32 , 40

Multiples of 12= 12 , 24 , 36 , 48 , 60

Here, 24 is the first common multiple of both 8 and 12.

Therefore, LCM (8 , 12) = 24

LCM of 8 and 12 by Long Division

Below are the steps for finding LCM of 8 and 12 by long division method:

Step 1: Divide the numbers, by the smallest prime number.

Step 2: If any number is not divisible, then write down that number and proceed further.

Step 3: Keep on dividing the row of numbers by prime numbers, unless we get the results as 1 in the complete row.

Step 4: Now LCM of the numbers will be equal to the product of all the prime numbers we obtained in the division method.

To calculate the LCM of 8 and 12 by the division method, we will divide the numbers by their prime factors as shown:

LCM = 2 × 2 × 2 × 3 = 24

LCM vs HCF of 8 and 12

Highest Common Factor of 8 and 12 is 4. It is the largest possible number which can divide 8 and 12 without leaving any remainder.

Least Common Multiple of 8 and 12 is 24. It is the smallest possible number which is divisible by 8 and 12 without leaving any remainder.

Also, LCM × HCF = Product of Two Numbers

8 = 2 × 2 × 2 = 2³

12 = 2 × 2 × 3 = 2² × 3

LCM (8, 12) = 2³ × 3 = 24

HCF (8, 12) = 2² = 4

LCM (8, 12) × HCF (8, 12) = 24 × 4 = 96…(i)

Product of Two Numbers = 8 × 12 = 96…(ii)

From equation (i) and equation (ii)

LCM (8, 12) × HCF (8, 12) = Product of 8 × 12

LCM Formula	HCF and LCM
LCM of 9 and 12	LCM of 6 and 9
LCM of 12 and 18	LCM of 8 and 10

Solved Example on LCM of 8 and 12

Some examples on LCM of 8 and 12

Example 1: Find the LCM if the product of two numbers is 96 and the GCD is 4.

Solution:

Given,

• Product of Two Numbers = 96
• GCD = 4

We know, LCM × GCD = Product of Two Numbers

LCM = Product/GCD

LCM = 96/4

LCM = 24

Example 2: Verify the relationship between GCF and LCM of 8 and 12.

Solution:

LCM(8, 12) × GCF(8, 12) = Product of 8, 12

8 = 2 × 2 × 2 = 2³

12 = 2 × 2 × 3 = 2² × 3

LCM (8, 12) = 2³ × 3= 24

HCF (8, 12) = 2² = 4

LCM (8, 12) × HCF (8, 12) = 24 × 4= 96

Product of 8, 12= 8 × 12= 96

Example 3: GCD and LCM of two numbers are 4 and 24 respectively. If one number is 8, find the other number.

Solution:

Let other number be x

GCD × LCM = 8 × x

x = (GCD × LCM)/8

x = (4 × 24)/8

x = 12

Therefore, the other number is 12.

Example 4: How to Find the LCM of 8 and 12 by Prime Factorization?

Solution:

8 = 2 × 2 × 2 = 2³

12 = 2 × 2 × 3 = 2² × 3

LCM (8, 12) = 24

Practice Questions on LCM of 8 and 12

Some practice problems on LCM of 8 and 12 are,

Q1. GCD and LCM of two numbers are 4 and 96 respectively. If one number is 24, find the other number.

Q2. Find LCM if the product of two numbers is 984 and the GCD is 24.

Q3. Find LCM of 92 and 118.

Q4. Find LCM and HCF of 27 and 96.

LCM of 8 and 12 Frequently Asked Questions

What is LCM of 8 and 12?

LCM of 8 and 12 is 24

What are Methods Used to Find LCM of 24 and 36.

The methods used to find the LCM of 24 and 36 are:

• Prime Factorization Method
• Division Method
• Listing Multiple Method

What is LCM?

LCM is the smallest common multiple which is divisible by given set of numbers without leaving any remainder.

What are the GCF and LCM of 8 and 12 respectively?

The Greatest Common Factor of 8 and 12 is 4 and the Least Common Multiple of 8 and 12 is 24.