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

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


The methods to find the LCM the 24 and also 36 are defined below.

By department MethodBy Listing MultiplesBy prime Factorization Method

LCM that 24 and also 36 by division Method

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

Step 3: proceed the actions until only 1s room left in the last row.

The LCM that 24 and also 36 is the product of all 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 calculation the LCM the 24 and also 36 by listing out the common multiples, we deserve 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 usual multiples from the multiples the 24 and also 36 space 72, 144, . . .Step 3: The smallest usual multiple the 24 and 36 is 72.

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

LCM that 24 and 36 by prime Factorization

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

☛ likewise Check:


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

Solution:

The relation between GCF and LCM the 24 and also 36 is provided as,LCM(24, 36) × GCF(24, 36) = Product of 24, 36Prime administer of 24 and also 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 2 numbers is 864. If their GCD is 12, what is their LCM?

Solution:

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


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FAQs ~ above LCM of 24 and 36

What is the LCM the 24 and also 36?

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

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

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

What room the techniques to uncover LCM that 24 and 36?

The frequently used approaches to find the LCM the 24 and 36 are:

Listing MultiplesPrime administer MethodDivision Method

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

To find the LCM that 24 and 36 utilizing prime factorization, we will find the element factors, (24 = 2 × 2 × 2 × 3) and also (36 = 2 × 2 × 3 × 3). LCM the 24 and also 36 is the product that prime factors raised to your respective highest exponent amongst the numbers 24 and 36.⇒ LCM the 24, 36 = 23 × 32 = 72.

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

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