LCM that 4, 6, and 8 is the smallest number among all usual multiples of 4, 6, and 8. The first couple of multiples of 4, 6, and 8 room (4, 8, 12, 16, 20 . . .), (6, 12, 18, 24, 30 . . .), and also (8, 16, 24, 32, 40 . . .) respectively. There space 3 commonly used approaches to discover LCM of 4, 6, 8 - by department method, by listing multiples, and also by prime factorization.

You are watching: What is the least common multiple of 4, 6 and 8

1.LCM of 4, 6, and also 8
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM that 4, 6, and 8 is 24.

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Explanation:

The LCM of three non-zero integers, a(4), b(6), and c(8), is the smallest optimistic integer m(24) that is divisible by a(4), b(6), and c(8) without any type of remainder.


Let's look at the different methods because that finding the LCM of 4, 6, and 8.

By element Factorization MethodBy Listing MultiplesBy department Method

LCM the 4, 6, and 8 by element Factorization

Prime administer of 4, 6, and 8 is (2 × 2) = 22, (2 × 3) = 21 × 31, and (2 × 2 × 2) = 23 respectively. LCM of 4, 6, and 8 can be obtained by multiply prime determinants raised to your respective highest power, i.e. 23 × 31 = 24.Hence, the LCM that 4, 6, and also 8 by element factorization is 24.

LCM the 4, 6, and 8 by Listing Multiples

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To calculate the LCM the 4, 6, 8 by listing out the typical multiples, we have the right to follow the given below steps:

Step 1: list a few multiples the 4 (4, 8, 12, 16, 20 . . .), 6 (6, 12, 18, 24, 30 . . .), and also 8 (8, 16, 24, 32, 40 . . .).Step 2: The typical multiples indigenous the multiples the 4, 6, and 8 are 24, 48, . . .Step 3: The smallest usual multiple the 4, 6, and also 8 is 24.

∴ The least typical multiple of 4, 6, and also 8 = 24.

LCM of 4, 6, and also 8 by department Method

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To calculation the LCM of 4, 6, and 8 by the department method, we will certainly divide the numbers(4, 6, 8) by their prime components (preferably common). The product of these divisors provides the LCM that 4, 6, and 8.

Step 2: If any of the given numbers (4, 6, 8) is a lot of of 2, division it through 2 and write the quotient below it. Lug down any number the is no divisible through the prime number.Step 3: continue the measures until just 1s are left in the last row.

The LCM of 4, 6, and 8 is the product of every prime numbers on the left, i.e. LCM(4, 6, 8) by division method = 2 × 2 × 2 × 3 = 24.

☛ also Check:


Example 1: Verify the relationship in between the GCD and also LCM that 4, 6, and 8.

Solution:

The relation in between GCD and LCM that 4, 6, and also 8 is given as,LCM(4, 6, 8) = <(4 × 6 × 8) × GCD(4, 6, 8)>/⇒ prime factorization that 4, 6 and also 8:

4 = 226 = 21 × 318 = 23

∴ GCD the (4, 6), (6, 8), (4, 8) and also (4, 6, 8) = 2, 2, 4 and 2 respectively.Now, LHS = LCM(4, 6, 8) = 24.And, RHS = <(4 × 6 × 8) × GCD(4, 6, 8)>/ = <(192) × 2>/<2 × 2 × 4> = 24LHS = RHS = 24.Hence verified.


Example 2: calculate the LCM of 4, 6, and also 8 making use of the GCD that the provided numbers.

Solution:

Prime administer of 4, 6, 8:

4 = 226 = 21 × 318 = 23

Therefore, GCD(4, 6) = 2, GCD(6, 8) = 2, GCD(4, 8) = 4, GCD(4, 6, 8) = 2We know,LCM(4, 6, 8) = <(4 × 6 × 8) × GCD(4, 6, 8)>/LCM(4, 6, 8) = (192 × 2)/(2 × 2 × 4) = 24⇒LCM(4, 6, 8) = 24


Example 3: find the the smallest number the is divisible by 4, 6, 8 exactly.

Solution:

The smallest number the is divisible by 4, 6, and 8 exactly is their LCM.⇒ Multiples the 4, 6, and also 8:

Multiples of 4 = 4, 8, 12, 16, 20, 24, . . . .Multiples the 6 = 6, 12, 18, 24, 30, 36, . . . .Multiples that 8 = 8, 16, 24, 32, 40, 48, . . . .

Therefore, the LCM the 4, 6, and also 8 is 24.


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FAQs top top LCM that 4, 6, and also 8

What is the LCM that 4, 6, and also 8?

The LCM that 4, 6, and also 8 is 24. To uncover the LCM (least usual multiple) of 4, 6, and also 8, we need to discover the multiples the 4, 6, and 8 (multiples that 4 = 4, 8, 12, 16, 24 . . . .; multiples the 6 = 6, 12, 18, 24 . . . .; multiples the 8 = 8, 16, 24, 32 . . . .) and choose the the smallest multiple that is specifically divisible through 4, 6, and also 8, i.e., 24.

What is the the very least Perfect Square Divisible through 4, 6, and 8?

The least number divisible through 4, 6, and also 8 = LCM(4, 6, 8)LCM the 4, 6, and also 8 = 2 × 2 × 2 × 3 ⇒ the very least perfect square divisible by every 4, 6, and also 8 = LCM(4, 6, 8) × 2 × 3 = 144 Therefore, 144 is the required number.

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How to discover the LCM of 4, 6, and also 8 by element Factorization?

To uncover the LCM the 4, 6, and also 8 making use of prime factorization, we will find the prime factors, (4 = 22), (6 = 21 × 31), and (8 = 23). LCM the 4, 6, and also 8 is the product of prime factors raised to their respective highest possible exponent among the numbers 4, 6, and also 8.⇒ LCM of 4, 6, 8 = 23 × 31 = 24.

What are the techniques to discover LCM of 4, 6, 8?

The generally used approaches to find the LCM the 4, 6, 8 are: