LCM the 3, 6, and 8 is the smallest number amongst all typical multiples of 3, 6, and 8. The first few multiples that 3, 6, and 8 space (3, 6, 9, 12, 15 . . .), (6, 12, 18, 24, 30 . . .), and also (8, 16, 24, 32, 40 . . .) respectively. There room 3 commonly used methods to uncover LCM the 3, 6, 8 - by listing multiples, by division method, and by element factorization.

You are watching: Lcm of 3 6 and 8

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

Answer: LCM the 3, 6, and also 8 is 24.

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Explanation:

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


Let's look at the different methods because that finding the LCM of 3, 6, and also 8.

By element Factorization MethodBy division MethodBy Listing Multiples

LCM of 3, 6, and 8 by prime Factorization

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

LCM of 3, 6, and 8 by division Method

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To calculation the LCM the 3, 6, and also 8 by the division method, we will divide the numbers(3, 6, 8) by your prime components (preferably common). The product of these divisors gives the LCM that 3, 6, and also 8.

Step 2: If any kind of of the offered numbers (3, 6, 8) is a lot of of 2, divide it through 2 and write the quotient below it. Lug down any type of number the is not divisible by the element number.Step 3: continue the procedures until just 1s room left in the critical row.

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

LCM of 3, 6, and also 8 by Listing Multiples

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To calculation the LCM of 3, 6, 8 by listing the end the common multiples, we deserve to follow the given listed below steps:

Step 1: perform a couple of multiples that 3 (3, 6, 9, 12, 15 . . .), 6 (6, 12, 18, 24, 30 . . .), and 8 (8, 16, 24, 32, 40 . . .).Step 2: The usual multiples from the multiples that 3, 6, and also 8 space 24, 48, . . .Step 3: The smallest usual multiple of 3, 6, and 8 is 24.

∴ The least typical multiple of 3, 6, and also 8 = 24.

☛ additionally Check:


Example 1: Verify the relationship between the GCD and also LCM the 3, 6, and also 8.

Solution:

The relation between GCD and also LCM that 3, 6, and 8 is offered as,LCM(3, 6, 8) = <(3 × 6 × 8) × GCD(3, 6, 8)>/⇒ prime factorization that 3, 6 and also 8:

3 = 316 = 21 × 318 = 23

∴ GCD the (3, 6), (6, 8), (3, 8) and (3, 6, 8) = 3, 2, 1 and also 1 respectively.Now, LHS = LCM(3, 6, 8) = 24.And, RHS = <(3 × 6 × 8) × GCD(3, 6, 8)>/ = <(144) × 1>/<3 × 2 × 1> = 24LHS = RHS = 24.Hence verified.


Example 2: discover the smallest number that is divisible through 3, 6, 8 exactly.

Solution:

The smallest number that is divisible by 3, 6, and 8 precisely is their LCM.⇒ Multiples the 3, 6, and also 8:

Multiples that 3 = 3, 6, 9, 12, 15, 18, 21, 24, . . . .Multiples the 6 = 6, 12, 18, 24, 30, . . . .Multiples that 8 = 8, 16, 24, 32, 40, . . . .

Therefore, the LCM the 3, 6, and 8 is 24.


Example 3: calculate the LCM of 3, 6, and 8 using the GCD the the offered numbers.

Solution:

Prime factorization of 3, 6, 8:

3 = 316 = 21 × 318 = 23

Therefore, GCD(3, 6) = 3, GCD(6, 8) = 2, GCD(3, 8) = 1, GCD(3, 6, 8) = 1We know,LCM(3, 6, 8) = <(3 × 6 × 8) × GCD(3, 6, 8)>/LCM(3, 6, 8) = (144 × 1)/(3 × 2 × 1) = 24⇒LCM(3, 6, 8) = 24


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FAQs ~ above LCM that 3, 6, and also 8

What is the LCM of 3, 6, and 8?

The LCM the 3, 6, and 8 is 24. To find the least common multiple that 3, 6, and also 8, we require to find the multiples of 3, 6, and 8 (multiples of 3 = 3, 6, 9, 12 . . . . 24 . . . . ; multiples that 6 = 6, 12, 18, 24 . . . .; multiples the 8 = 8, 16, 24, 32 . . . .) and also choose the the smallest multiple that is specifically divisible by 3, 6, and 8, i.e., 24.

How to uncover the LCM of 3, 6, and 8 by element Factorization?

To discover the LCM the 3, 6, and 8 using prime factorization, we will uncover the prime factors, (3 = 31), (6 = 21 × 31), and (8 = 23). LCM that 3, 6, and 8 is the product that prime determinants raised to your respective highest exponent among the numbers 3, 6, and 8.⇒ LCM that 3, 6, 8 = 23 × 31 = 24.

What is the least Perfect Square Divisible by 3, 6, and 8?

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

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What is the Relation between GCF and also LCM the 3, 6, 8?

The adhering to equation have the right to be provided to to express the relation between GCF and also LCM that 3, 6, 8, i.e. LCM(3, 6, 8) = <(3 × 6 × 8) × GCF(3, 6, 8)>/.