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.

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

Answer: LCM of 24 and 36 is 72.

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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.


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

By Division MethodBy Listing MultiplesBy Prime Factorization Method

LCM of 24 and 36 by Division Method

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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 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

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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:


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, 36Prime factorization of 24 and 36 is given as, 24 = (2 × 2 × 2 × 3) = 23 × 31 and 36 = (2 × 2 × 3 × 3) = 22 × 32LCM(24, 36) = 72GCF(24, 36) = 12LHS = LCM(24, 36) × GCF(24, 36) = 72 × 12 = 864RHS = Product of 24, 36 = 24 × 36 = 864⇒ LHS = RHS = 864Hence, verified.


Example 3: The product of two numbers is 864. If their GCD is 12, what is their LCM?

Solution:

Given: GCD = 12product of numbers = 864∵ LCM × GCD = product of numbers⇒ LCM = Product/GCD = 864/12Therefore, 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 ⇒ Least perfect square divisible by each 24 and 36 = LCM(24, 36) × 2 = 144 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 MultiplesPrime Factorization MethodDivision 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.

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