LCM of 24 and also 36 is the the smallest number among all usual multiples of 24 and 36. The first few multiples the 24 and 36 are (24, 48, 72, 96, . . . ) and (36, 72, 108, 144, . . . ) respectively. There space 3 commonly used techniques to discover LCM that 24 and 36 - by department 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 that 24 and also 36 is 72.

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Explanation:

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


The techniques to uncover the LCM the 24 and also 36 are described below.

By department MethodBy Listing MultiplesBy prime Factorization Method

LCM of 24 and 36 by division Method

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To calculation the LCM the 24 and also 36 by the department method, we will certainly divide the numbers(24, 36) by their prime determinants (preferably common). The product of these divisors provides the LCM the 24 and 36.

Step 3: continue the steps until just 1s space left in the last row.

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

LCM the 24 and also 36 by Listing Multiples

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To calculate the LCM the 24 and 36 through listing out the typical multiples, we can follow the given below steps:

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

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

LCM that 24 and also 36 by prime Factorization

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

☛ also Check:


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

Solution:

The relation in between GCF and LCM that 24 and 36 is provided as,LCM(24, 36) × GCF(24, 36) = Product that 24, 36Prime administer of 24 and 36 is provided 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 the 24, 36 = 24 × 36 = 864⇒ LHS = RHS = 864Hence, verified.


Example 3: The product of 2 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 combination for the given instance is LCM(24, 36) = 72.


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FAQs ~ above LCM the 24 and 36

What is the LCM that 24 and 36?

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

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

The the very least number divisible by 24 and also 36 = LCM(24, 36)LCM of 24 and 36 = 2 × 2 × 2 × 3 × 3 ⇒ the very least perfect square divisible by each 24 and also 36 = LCM(24, 36) × 2 = 144 Therefore, 144 is the forced number.

What are the techniques to discover LCM that 24 and also 36?

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

Listing MultiplesPrime factorization MethodDivision Method

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

To discover the LCM of 24 and 36 making use of prime factorization, us will find the element factors, (24 = 2 × 2 × 2 × 3) and (36 = 2 × 2 × 3 × 3). LCM of 24 and also 36 is the product that prime factors raised to their respective highest exponent amongst the numbers 24 and 36.⇒ LCM the 24, 36 = 23 × 32 = 72.

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

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