LCM the 2, 6, and 8 is the the smallest number among all usual multiples that 2, 6, and 8. The first couple of multiples that 2, 6, and 8 space (2, 4, 6, 8, 10 . . .), (6, 12, 18, 24, 30 . . .), and also (8, 16, 24, 32, 40 . . .) respectively. There room 3 commonly used methods to uncover LCM that 2, 6, 8 - by listing multiples, by element factorization, and by department method.

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

Answer: LCM the 2, 6, and also 8 is 24.

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Explanation:

The LCM of 3 non-zero integers, a(2), b(6), and c(8), is the smallest positive integer m(24) that is divisible by a(2), b(6), and c(8) without any type of remainder.


The techniques to find the LCM the 2, 6, and also 8 are defined below.

By Listing MultiplesBy element Factorization MethodBy division Method

LCM the 2, 6, and 8 through Listing Multiples

To calculate the LCM the 2, 6, 8 through listing out the usual multiples, we can follow the given listed below steps:

Step 1: perform a few multiples the 2 (2, 4, 6, 8, 10 . . .), 6 (6, 12, 18, 24, 30 . . .), and 8 (8, 16, 24, 32, 40 . . .).Step 2: The usual multiples indigenous the multiples that 2, 6, and 8 room 24, 48, . . .Step 3: The smallest usual multiple the 2, 6, and 8 is 24.

∴ The least common multiple that 2, 6, and also 8 = 24.

LCM of 2, 6, and 8 by element Factorization

Prime factorization of 2, 6, and also 8 is (2) = 21, (2 × 3) = 21 × 31, and also (2 × 2 × 2) = 23 respectively. LCM the 2, 6, and also 8 can be obtained by multiplying prime components raised to your respective greatest power, i.e. 23 × 31 = 24.Hence, the LCM the 2, 6, and also 8 by element factorization is 24.

LCM of 2, 6, and 8 by division Method

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To calculation the LCM that 2, 6, and 8 by the department method, we will certainly divide the numbers(2, 6, 8) by your prime components (preferably common). The product of these divisors offers the LCM the 2, 6, and also 8.

Step 2: If any of the offered numbers (2, 6, 8) is a multiple of 2, division it by 2 and write the quotient below it. Bring down any kind of number the is not divisible by the element number.Step 3: continue the procedures until only 1s are left in the critical row.

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

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Example 2: Verify the relationship between the GCD and LCM of 2, 6, and also 8.

Solution:

The relation between GCD and also LCM the 2, 6, and 8 is offered as,LCM(2, 6, 8) = <(2 × 6 × 8) × GCD(2, 6, 8)>/⇒ prime factorization of 2, 6 and also 8:

2 = 216 = 21 × 318 = 23

∴ GCD that (2, 6), (6, 8), (2, 8) and (2, 6, 8) = 2, 2, 2 and also 2 respectively.Now, LHS = LCM(2, 6, 8) = 24.And, RHS = <(2 × 6 × 8) × GCD(2, 6, 8)>/ = <(96) × 2>/<2 × 2 × 2> = 24LHS = RHS = 24.Hence verified.


Example 3: calculation the LCM of 2, 6, and also 8 making use of the GCD the the given numbers.

Solution:

Prime administrate of 2, 6, 8:

2 = 216 = 21 × 318 = 23

Therefore, GCD(2, 6) = 2, GCD(6, 8) = 2, GCD(2, 8) = 2, GCD(2, 6, 8) = 2We know,LCM(2, 6, 8) = <(2 × 6 × 8) × GCD(2, 6, 8)>/LCM(2, 6, 8) = (96 × 2)/(2 × 2 × 2) = 24⇒LCM(2, 6, 8) = 24


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FAQs top top LCM of 2, 6, and also 8

What is the LCM the 2, 6, and 8?

The LCM that 2, 6, and 8 is 24. To find the LCM (least typical multiple) the 2, 6, and 8, we need to uncover the multiples the 2, 6, and also 8 (multiples that 2 = 2, 4, 6, 8 . . . . 24 . . . . ; multiples the 6 = 6, 12, 18, 24 . . . .; multiples of 8 = 8, 16, 24, 32 . . . .) and choose the the smallest multiple the is precisely divisible by 2, 6, and 8, i.e., 24.

How to uncover the LCM of 2, 6, and 8 by element Factorization?

To uncover the LCM of 2, 6, and 8 using prime factorization, we will find the prime factors, (2 = 21), (6 = 21 × 31), and also (8 = 23). LCM the 2, 6, and 8 is the product that prime components raised to their respective highest exponent amongst the number 2, 6, and 8.⇒ LCM of 2, 6, 8 = 23 × 31 = 24.

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What room the techniques to find LCM that 2, 6, 8?

The typically used techniques to find the LCM that 2, 6, 8 are:

Prime factorization MethodListing MultiplesDivision Method

What is the the very least Perfect Square Divisible by 2, 6, and also 8?

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