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LCM of 24 and 36

LCM of 24 and 36 is the smallest number among all common multiples of 24 and 36. The first few multiples of 24 and 36 are (24, 48, 72, 96, . . . ) and (36, 72, 108, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 24 and 36 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 24 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 24 and 36?

Answer: LCM of 24 and 36 is 72.

Explanation:

The LCM of two non-zero integers, x(24) and y(36), is the smallest positive integer m(72) that is divisible by both x(24) and y(36) without any remainder.

Methods to Find LCM of 24 and 36

The methods to find the LCM of 24 and 36 are explained below.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 24 and 36 by Division Method

To calculate the LCM of 24 and 36 by the division method, we will divide the numbers(24, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 24 and 36.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 24 and 36. Write this prime number(2) on the left of the given numbers(24 and 36), separated as per the ladder arrangement.
Step 2: If any of the given numbers (24, 36) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 24 and 36 is the product of all prime numbers on the left, i.e. LCM(24, 36) by division method = 2 × 2 × 2 × 3 × 3 = 72.

LCM of 24 and 36 by Listing Multiples

To calculate the LCM of 24 and 36 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 24 (24, 48, 72, 96, . . . ) and 36 (36, 72, 108, 144, . . . . )
Step 2: The common multiples from the multiples of 24 and 36 are 72, 144, . . .
Step 3: The smallest common multiple of 24 and 36 is 72.

∴ The least common multiple of 24 and 36 = 72.

LCM of 24 and 36 by Prime Factorization

Prime factorization of 24 and 36 is (2 × 2 × 2 × 3) = 2³ × 3¹ and (2 × 2 × 3 × 3) = 2² × 3² respectively. LCM of 24 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² = 72.
Hence, the LCM of 24 and 36 by prime factorization is 72.

☛ Also Check:

LCM of 24 and 36 Examples

Example 1: Verify the relationship between GCF and LCM of 24 and 36.

Solution:

The relation between GCF and LCM of 24 and 36 is given as,
LCM(24, 36) × GCF(24, 36) = Product of 24, 36
Prime factorization of 24 and 36 is given as, 24 = (2 × 2 × 2 × 3) = 2³ × 3¹ and 36 = (2 × 2 × 3 × 3) = 2² × 3²
LCM(24, 36) = 72
GCF(24, 36) = 12
LHS = LCM(24, 36) × GCF(24, 36) = 72 × 12 = 864
RHS = Product of 24, 36 = 24 × 36 = 864
⇒ LHS = RHS = 864
Hence, verified.
Example 2: The GCD and LCM of two numbers are 12 and 72 respectively. If one number is 24, find the other number.

Solution:

Let the other number be y.
∵ GCD × LCM = 24 × y
⇒ y = (GCD × LCM)/24
⇒ y = (12 × 72)/24
⇒ y = 36
Therefore, the other number is 36.
Example 3: The product of two numbers is 864. If their GCD is 12, what is their LCM?

Solution:

Given: GCD = 12
product of numbers = 864
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 864/12
Therefore, the LCM is 72.
The probable combination for the given case is LCM(24, 36) = 72.

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FAQs on LCM of 24 and 36

What is the LCM of 24 and 36?

The LCM of 24 and 36 is 72. To find the least common multiple of 24 and 36, we need to find the multiples of 24 and 36 (multiples of 24 = 24, 48, 72, 96; multiples of 36 = 36, 72, 108, 144) and choose the smallest multiple that is exactly divisible by 24 and 36, i.e., 72.

What is the Least Perfect Square Divisible by 24 and 36?

The least number divisible by 24 and 36 = LCM(24, 36)
LCM of 24 and 36 = 2 × 2 × 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 24 and 36 = LCM(24, 36) × 2 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

What are the Methods to Find LCM of 24 and 36?

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

Listing Multiples
Prime Factorization Method
Division Method

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

To find the LCM of 24 and 36 using prime factorization, we will find the prime factors, (24 = 2 × 2 × 2 × 3) and (36 = 2 × 2 × 3 × 3). LCM of 24 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 24 and 36.
⇒ LCM of 24, 36 = 2³ × 3² = 72.

If the LCM of 36 and 24 is 72, Find its GCF.

LCM(36, 24) × GCF(36, 24) = 36 × 24
Since the LCM of 36 and 24 = 72
⇒ 72 × GCF(36, 24) = 864
Therefore, the GCF = 864/72 = 12.

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