LCM of 24 and also 36 is the smallest number amongst all typical multiples that 24 and 36. The first few multiples of 24 and 36 are (24, 48, 72, 96, . . . ) and also (36, 72, 108, 144, . . . ) respectively. There are 3 frequently used approaches to find LCM that 24 and also 36 - by division method, by element factorization, and by listing multiples.

You are watching: What is the least common multiple of 24 and 36

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

Answer: LCM of 24 and 36 is 72.

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Explanation:

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


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

By division MethodBy Listing MultiplesBy prime Factorization Method

LCM of 24 and 36 by department Method

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

Step 3: proceed the steps until only 1s room left in the critical row.

The LCM of 24 and also 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 the 24 and also 36 through Listing Multiples

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To calculation the LCM of 24 and also 36 through listing out the common multiples, we can follow the given listed below steps:

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

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

LCM that 24 and also 36 by prime Factorization

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

☛ likewise Check:


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

Solution:

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

Solution:

Given: GCD = 12product of number = 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 on LCM that 24 and also 36

What is the LCM of 24 and also 36?

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

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

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

What room the methods to find LCM the 24 and also 36?

The frequently used methods to uncover the LCM of 24 and 36 are:

Listing MultiplesPrime factorization MethodDivision Method

How to uncover the LCM the 24 and 36 by element Factorization?

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

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

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