LCM that 4, 8, and 12 is the smallest number amongst all common multiples of 4, 8, and also 12. The first few multiples of 4, 8, and also 12 space (4, 8, 12, 16, 20 . . .), (8, 16, 24, 32, 40 . . .), and also (12, 24, 36, 48, 60 . . .) respectively. There space 3 frequently used approaches to uncover LCM that 4, 8, 12 - by listing multiples, by division method, and also by element factorization.

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1.LCM the 4, 8, and 12
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM of 4, 8, and 12 is 24.

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Explanation:

The LCM of three non-zero integers, a(4), b(8), and c(12), is the smallest positive integer m(24) the is divisible through a(4), b(8), and c(12) without any remainder.


The methods to find the LCM that 4, 8, and also 12 are defined below.

By division MethodBy prime Factorization MethodBy Listing Multiples

LCM of 4, 8, and also 12 by department Method

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To calculation the LCM of 4, 8, and also 12 by the division method, we will certainly divide the numbers(4, 8, 12) by your prime components (preferably common). The product of these divisors offers the LCM the 4, 8, and also 12.

Step 2: If any of the given numbers (4, 8, 12) is a many of 2, division it by 2 and write the quotient below it. Carry down any kind of number that is not divisible by the element number.Step 3: continue the procedures until only 1s room left in the last row.

The LCM of 4, 8, and 12 is the product of all prime numbers on the left, i.e. LCM(4, 8, 12) by department method = 2 × 2 × 2 × 3 = 24.

LCM the 4, 8, and also 12 by prime Factorization

Prime factorization of 4, 8, and also 12 is (2 × 2) = 22, (2 × 2 × 2) = 23, and also (2 × 2 × 3) = 22 × 31 respectively. LCM the 4, 8, and also 12 can be acquired by multiplying prime determinants raised to their respective greatest power, i.e. 23 × 31 = 24.Hence, the LCM the 4, 8, and also 12 by prime factorization is 24.

LCM that 4, 8, and also 12 by Listing Multiples

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To calculation the LCM of 4, 8, 12 by listing out the common multiples, we have the right to follow the given below steps:

Step 1: list a couple of multiples that 4 (4, 8, 12, 16, 20 . . .), 8 (8, 16, 24, 32, 40 . . .), and also 12 (12, 24, 36, 48, 60 . . .).Step 2: The common multiples native the multiples that 4, 8, and also 12 are 24, 48, . . .Step 3: The smallest usual multiple that 4, 8, and also 12 is 24.

∴ The least usual multiple of 4, 8, and 12 = 24.

☛ likewise Check:


Example 1: Verify the relationship in between the GCD and LCM the 4, 8, and also 12.

Solution:

The relation in between GCD and LCM the 4, 8, and also 12 is provided as,LCM(4, 8, 12) = <(4 × 8 × 12) × GCD(4, 8, 12)>/⇒ prime factorization the 4, 8 and also 12:

4 = 228 = 2312 = 22 × 31

∴ GCD of (4, 8), (8, 12), (4, 12) and (4, 8, 12) = 4, 4, 4 and 4 respectively.Now, LHS = LCM(4, 8, 12) = 24.And, RHS = <(4 × 8 × 12) × GCD(4, 8, 12)>/ = <(384) × 4>/<4 × 4 × 4> = 24LHS = RHS = 24.Hence verified.


Example 2: calculate the LCM the 4, 8, and 12 utilizing the GCD of the given numbers.

Solution:

Prime factorization of 4, 8, 12:

4 = 228 = 2312 = 22 × 31

Therefore, GCD(4, 8) = 4, GCD(8, 12) = 4, GCD(4, 12) = 4, GCD(4, 8, 12) = 4We know,LCM(4, 8, 12) = <(4 × 8 × 12) × GCD(4, 8, 12)>/LCM(4, 8, 12) = (384 × 4)/(4 × 4 × 4) = 24⇒LCM(4, 8, 12) = 24


Example 3: uncover the the smallest number the is divisible by 4, 8, 12 exactly.

Solution:

The smallest number the is divisible by 4, 8, and also 12 specifically is your LCM.⇒ Multiples of 4, 8, and 12:

Multiples the 4 = 4, 8, 12, 16, 20, 24, 28, . . . .Multiples the 8 = 8, 16, 24, 32, 40, 48, 56, . . . .Multiples that 12 = 12, 24, 36, 48, 60, 72, 84, . . . .

Therefore, the LCM of 4, 8, and 12 is 24.


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FAQs ~ above LCM that 4, 8, and 12

What is the LCM that 4, 8, and also 12?

The LCM the 4, 8, and 12 is 24. To uncover the LCM (least common multiple) that 4, 8, and 12, we require to discover the multiples the 4, 8, and also 12 (multiples that 4 = 4, 8, 12, 16, 24 . . . .; multiples of 8 = 8, 16, 24, 32 . . . .; multiples of 12 = 12, 24, 36, 48 . . . .) and also choose the smallest multiple that is specifically divisible through 4, 8, and 12, i.e., 24.

What is the Relation between GCF and LCM the 4, 8, 12?

The complying with equation can be used to refer the relation in between GCF and LCM that 4, 8, 12, i.e. LCM(4, 8, 12) = <(4 × 8 × 12) × GCF(4, 8, 12)>/.

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What room the methods to uncover LCM that 4, 8, 12?

The typically used approaches to discover the LCM the 4, 8, 12 are:

Listing MultiplesDivision MethodPrime factorization Method

How to discover the LCM of 4, 8, and also 12 by element Factorization?

To discover the LCM of 4, 8, and 12 utilizing prime factorization, we will find the element factors, (4 = 22), (8 = 23), and also (12 = 22 × 31). LCM the 4, 8, and also 12 is the product the prime factors raised to their respective highest possible exponent amongst the numbers 4, 8, and 12.⇒ LCM that 4, 8, 12 = 23 × 31 = 24.