LCM of 24 and 36

LCM of 24 and 36 is 72. LCM of two non-zero integers, 24 and 36, is the smallest positive integer 72 which is divisible by both 24 and 36 with no remainder.

In this article, we will learn about what is the LCM of 24 and 36, What is LCM, and How to Find LCM of 24 and 36 using various methods like Prime factorization, Listing Multiples, and By Long Division Method.

What is LCM of 24 and 36?

LCM of 24 and 36 is 72

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

Proceeding further we must first know What is LCM?

What is LCM?

Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers. LCM of two numbers is the value that is evenly divisible by the given two numbers. Let us take two numbers, 2 and 5.

• Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20…
• Multiples of 5 are 5, 10, 15, 20…

LCM of two numbers is the value that is evenly divisible by the given two numbers. In other words, it is the smallest number we get among the common multiples of both numbers.

We can see that the first common multiple for both 2 and 5 is 10. Therefore, the LCM of 2 and 5 is 10.

LCM of 24 and 36 Calculator

How to Find LCM of 24 and 36

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

• LCM of 24 and 36 by Prime Factorization

• LCM of 24 and 36 by Listing Multiples

• LCM of 24 and 36 by Long Division

LCM of 24 and 36 by Prime Factorization

Below are the steps for finding LCM of 24 and 36 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 24 and 36, respectively, are,

24 = 2 × 2 × 2 × 3 = 2³ × 3

36 = 2 × 2 × 3 × 3 = 2² × 3²

LCM (24, 36) = 2 × 2 × 2 × 3 × 3 = 2³ × 3² = 72

Learn more about, Prime Factorization Method

LCM of 24 and 36 by Listing Multiples

Below are the steps for finding LCM of 24 and 36 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 24 and 36 by listing out the common multiples, list the multiples as:

Multiples of 24 = 24, 48, 72, 96, 120

Multiples of 36 = 36, 72, 109, 144, 180

Here, 72 is the first common multiple of both 24 and 36.

Therefore, LCM (24, 36) = 72

LCM of 24 and 36 by Long Division

Below are the steps for finding LCM of 24 and 36 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 24 and 36 by the division method, we will divide the numbers by their prime factors as shown:

LCM = 2 × 2 × 2 × 3 × 3 × 1 × 1 = 72

LCM and HCF of 24 and 36

Highest Common Factor of 24 and 36 is 12 and the Least Common Multiple of 24 and 36 is 72.

Also, LCM × HCF = Product of Two Numbers

24 = 2 × 2 × 2 × 3 = 2³ × 3

36 = 2 × 2 × 3 × 3 = 2² × 3²

LCM (24, 36) = 2³ × 3² = 72

HCF (24, 36) = 3 × 2² = 12

LCM (24, 36) × HCF (24, 36) = 12 × 72 = 864…(i)

Product of Two Numbers = 24 × 36 = 864…(ii)

From eq(i) and eq(ii)

LCM (24, 36) × HCF (24, 36) = Product of 24 × 36

Example on LCM of 24 and 36

Some examples on LCM of 24 and 36

Example 1. Find the LCM if the product of two numbers is 864 and the GCD is 12.

Solution:

Given,

• Product of Two Numbers = 864
• GCD = 12

We know, LCM × GCD = Product of Two Numbers

LCM = Product/GCD

LCM = 864/12

LCM = 72

Example 2. Verify the relationship between GCF and LCM of 24 and 36.

Solution:

LCM(24, 36) × GCF(24, 36) = Product of 24, 36

• 24 = 2 × 2 × 2 × 3 = 2³ × 3
• 36 = 2 × 2 × 3 × 3 = 2² × 3²

LCM(24, 36) = 72

GCF(24, 36) = 12

LCM(24, 36) × GCF(24, 36) = 72 × 12 = 864

Product of 24, 36 = 24 × 36 = 864

Example 3. GCD and LCM of two numbers are 12 and 72 respectively. If one number is 24, find the other number.

Solution:

Let other number be x

GCD × LCM = 24 × x

x = (GCD × LCM)/24

x = (12 × 72)/24

x = 36

Therefore, the other number is 36.

Example 4. How to Find the LCM of 24 and 36 by Prime Factorization?

Solution:

24 = 2 x 2 x 2 x 3 = 2³ x 3

36 = 2 x 2 x 3 x 3 = 2² x 3²

LCM (24, 36) = 72

Practice Problems on LCM of 24 and 36

Some practice problems on LCM of 24 and 36 are,

P1. GCD and LCM of two numbers are 22 and 94 respectively. If one number is 24, find the other number.

P2. Find LCM if the product of two numbers is 984 and the GCD is 24.

P3. Find LCM of 92 and 118.

P4. Find LCM and HCF of 27 and 96.

FAQs on LCM of 24 and 36

What is LCM of 24 and 36?

LCM of 24 and 36 is 72.

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 are the GCF and LCM of 24 and 36 respectively?

The Greatest Common Factor of 24 and 36 is 12 and the Least Common Multiple of 24 and 36 is 72.