LCM the 6, 8, and also 12 is the the smallest number among all usual multiples of 6, 8, and 12. The first couple of multiples that 6, 8, and also 12 room (6, 12, 18, 24, 30 . . .), (8, 16, 24, 32, 40 . . .), and also (12, 24, 36, 48, 60 . . .) respectively. There room 3 typically used approaches to find LCM the 6, 8, 12 - by prime factorization, by listing multiples, and by department method.

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 1 LCM the 6, 8, and also 12 2 List that Methods 3 Solved Examples 4 FAQs

Answer: LCM that 6, 8, and 12 is 24. Explanation:

The LCM of three non-zero integers, a(6), b(8), and c(12), is the smallest positive integer m(24) that is divisible by a(6), b(8), and also c(12) without any type of remainder.

The techniques to discover the LCM of 6, 8, and also 12 are described below.

By department MethodBy Listing MultiplesBy element Factorization Method

### LCM of 6, 8, and 12 by department Method To calculation the LCM that 6, 8, and also 12 through the department method, we will certainly divide the numbers(6, 8, 12) by their prime determinants (preferably common). The product of this divisors provides the LCM of 6, 8, and also 12.

Step 2: If any type of of the given numbers (6, 8, 12) is a lot of of 2, divide it by 2 and also write the quotient below it. Bring down any kind of number that is no divisible through the element number.Step 3: proceed the actions until just 1s are left in the last row.

The LCM that 6, 8, and 12 is the product of all prime number on the left, i.e. LCM(6, 8, 12) by division method = 2 × 2 × 2 × 3 = 24.

### LCM that 6, 8, and 12 by Listing Multiples To calculate the LCM of 6, 8, 12 by listing the end the typical multiples, we deserve to follow the given below steps:

Step 1: perform a couple of multiples the 6 (6, 12, 18, 24, 30 . . .), 8 (8, 16, 24, 32, 40 . . .), and also 12 (12, 24, 36, 48, 60 . . .).Step 2: The usual multiples indigenous the multiples that 6, 8, and 12 are 24, 48, . . .Step 3: The smallest typical multiple the 6, 8, and 12 is 24.

∴ The least usual multiple the 6, 8, and also 12 = 24.

### LCM of 6, 8, and also 12 by element Factorization

Prime administer of 6, 8, and also 12 is (2 × 3) = 21 × 31, (2 × 2 × 2) = 23, and (2 × 2 × 3) = 22 × 31 respectively. LCM of 6, 8, and 12 can be obtained by multiplying prime factors raised to your respective highest power, i.e. 23 × 31 = 24.Hence, the LCM of 6, 8, and also 12 by element factorization is 24.

☛ likewise Check:

Example 3: Verify the relationship between the GCD and LCM of 6, 8, and 12.

Solution:

The relation between GCD and LCM that 6, 8, and also 12 is offered as,LCM(6, 8, 12) = <(6 × 8 × 12) × GCD(6, 8, 12)>/⇒ prime factorization that 6, 8 and 12:

6 = 21 × 318 = 2312 = 22 × 31

∴ GCD the (6, 8), (8, 12), (6, 12) and (6, 8, 12) = 2, 4, 6 and also 2 respectively.Now, LHS = LCM(6, 8, 12) = 24.And, RHS = <(6 × 8 × 12) × GCD(6, 8, 12)>/ = <(576) × 2>/<2 × 4 × 6> = 24LHS = RHS = 24.Hence verified. ## FAQs top top LCM the 6, 8, and also 12

### What is the LCM of 6, 8, and also 12?

The LCM that 6, 8, and also 12 is 24. To find the least typical multiple (LCM) that 6, 8, and 12, we need to find the multiples the 6, 8, and also 12 (multiples of 6 = 6, 12, 18 . . . .; multiples of 8 = 8, 16, 24 . . . .; multiples the 12 = 12, 24, 36 . . . .) and choose the the smallest multiple that is specifically divisible through 6, 8, and 12, i.e., 24.

### Which the the complying with is the LCM the 6, 8, and also 12? 50, 24, 120, 30

The worth of LCM that 6, 8, 12 is the smallest typical multiple of 6, 8, and also 12. The number satisfying the given condition is 24.

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### What are the techniques to uncover LCM that 6, 8, 12?

The frequently used approaches to find the LCM the 6, 8, 12 are: