LCM that 24 and also 36 is the smallest number among all common multiples the 24 and 36. The first couple of multiples of 24 and 36 room (24, 48, 72, 96, . . . ) and also (36, 72, 108, 144, . . . ) respectively. There room 3 commonly used methods to uncover LCM of 24 and 36 - by division method, by element factorization, and by listing multiples.

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

Answer: LCM the 24 and 36 is 72.

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Explanation:

The LCM of 2 non-zero integers, x(24) and also y(36), is the smallest confident integer m(72) that is divisible by both x(24) and also y(36) without any kind of remainder.


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

By division MethodBy Listing MultiplesBy element Factorization Method

LCM the 24 and 36 by division Method

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To calculate the LCM the 24 and also 36 by the division method, we will divide the numbers(24, 36) by their prime components (preferably common). The product of this divisors provides the LCM the 24 and 36.

Step 3: continue the measures until just 1s are left in the critical row.

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

LCM that 24 and 36 by Listing Multiples

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To calculation the LCM the 24 and 36 through listing out the common multiples, we have the right to follow the given below steps:

Step 1: perform a couple of multiples the 24 (24, 48, 72, 96, . . . ) and 36 (36, 72, 108, 144, . . . . )Step 2: The common multiples from the multiples the 24 and also 36 room 72, 144, . . .Step 3: The smallest typical multiple the 24 and 36 is 72.

∴ The least usual multiple that 24 and also 36 = 72.

LCM of 24 and also 36 by element Factorization

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

☛ additionally Check:


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

Solution:

The relation in between GCF and LCM that 24 and also 36 is offered as,LCM(24, 36) × GCF(24, 36) = Product the 24, 36Prime administer of 24 and 36 is provided as, 24 = (2 × 2 × 2 × 3) = 23 × 31 and also 36 = (2 × 2 × 3 × 3) = 22 × 32LCM(24, 36) = 72GCF(24, 36) = 12LHS = LCM(24, 36) × GCF(24, 36) = 72 × 12 = 864RHS = Product that 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 the numbers⇒ LCM = Product/GCD = 864/12Therefore, the LCM is 72.The probable mix for the given case is LCM(24, 36) = 72.


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FAQs top top LCM that 24 and 36

What is the LCM of 24 and also 36?

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

What is the least Perfect Square Divisible through 24 and also 36?

The least number divisible through 24 and 36 = LCM(24, 36)LCM that 24 and 36 = 2 × 2 × 2 × 3 × 3 ⇒ least perfect square divisible by every 24 and 36 = LCM(24, 36) × 2 = 144 Therefore, 144 is the required number.

What are the approaches to uncover LCM that 24 and also 36?

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

Listing MultiplesPrime factorization MethodDivision Method

How to discover the LCM that 24 and also 36 by prime Factorization?

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

If the LCM the 36 and also 24 is 72, discover its GCF.

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