LCM of 3, 8, and 12 is the the smallest number among all typical multiples of 3, 8, and also 12. The first couple of multiples the 3, 8, and 12 room (3, 6, 9, 12, 15 . . .), (8, 16, 24, 32, 40 . . .), and also (12, 24, 36, 48, 60 . . .) respectively. There space 3 typically used methods to discover LCM of 3, 8, 12 - through listing multiples, by division method, and also by prime factorization.

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

Answer: LCM the 3, 8, and 12 is 24.

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Explanation:

The LCM of three non-zero integers, a(3), b(8), and also c(12), is the smallest positive integer m(24) that is divisible by a(3), b(8), and c(12) without any type of remainder.


The approaches to find the LCM of 3, 8, and also 12 are described below.

By Listing MultiplesBy department MethodBy element Factorization Method

LCM that 3, 8, and also 12 by Listing Multiples

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To calculation the LCM the 3, 8, 12 by listing the end the usual multiples, we have the right to follow the given below steps:

Step 1: perform a couple of multiples the 3 (3, 6, 9, 12, 15 . . .), 8 (8, 16, 24, 32, 40 . . .), and also 12 (12, 24, 36, 48, 60 . . .).Step 2: The typical multiples indigenous the multiples the 3, 8, and also 12 room 24, 48, . . .Step 3: The smallest common multiple the 3, 8, and also 12 is 24.

∴ The least common multiple the 3, 8, and also 12 = 24.

LCM the 3, 8, and also 12 by department Method

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To calculate the LCM that 3, 8, and 12 by the division method, we will divide the numbers(3, 8, 12) by your prime components (preferably common). The product of this divisors provides the LCM that 3, 8, and 12.

Step 2: If any type of of the given numbers (3, 8, 12) is a many of 2, division it through 2 and write the quotient below it. Bring down any type of number that is no divisible by the element number.Step 3: proceed the measures until only 1s are left in the last row.

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

LCM of 3, 8, and also 12 by prime Factorization

Prime administrate of 3, 8, and also 12 is (3) = 31, (2 × 2 × 2) = 23, and (2 × 2 × 3) = 22 × 31 respectively. LCM of 3, 8, and 12 deserve to be derived by multiply prime components raised to their respective highest power, i.e. 23 × 31 = 24.Hence, the LCM of 3, 8, and 12 by element factorization is 24.

☛ additionally Check:


Example 1: Verify the relationship in between the GCD and also LCM the 3, 8, and 12.

Solution:

The relation in between GCD and also LCM that 3, 8, and also 12 is provided as,LCM(3, 8, 12) = <(3 × 8 × 12) × GCD(3, 8, 12)>/⇒ prime factorization the 3, 8 and also 12:

3 = 318 = 2312 = 22 × 31

∴ GCD that (3, 8), (8, 12), (3, 12) and also (3, 8, 12) = 1, 4, 3 and 1 respectively.Now, LHS = LCM(3, 8, 12) = 24.And, RHS = <(3 × 8 × 12) × GCD(3, 8, 12)>/ = <(288) × 1>/<1 × 4 × 3> = 24LHS = RHS = 24.Hence verified.


Example 2: calculate the LCM that 3, 8, and also 12 making use of the GCD that the provided numbers.

Solution:

Prime factorization of 3, 8, 12:

3 = 318 = 2312 = 22 × 31

Therefore, GCD(3, 8) = 1, GCD(8, 12) = 4, GCD(3, 12) = 3, GCD(3, 8, 12) = 1We know,LCM(3, 8, 12) = <(3 × 8 × 12) × GCD(3, 8, 12)>/LCM(3, 8, 12) = (288 × 1)/(1 × 4 × 3) = 24⇒LCM(3, 8, 12) = 24


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

Solution:

The smallest number the is divisible through 3, 8, and 12 exactly is your LCM.⇒ Multiples that 3, 8, and also 12:

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, . . . .Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, . . . .Multiples that 12 = 12, 24, 36, 48, 60, 72, 84, . . . .

Therefore, the LCM that 3, 8, and 12 is 24.


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FAQs ~ above LCM that 3, 8, and 12

What is the LCM that 3, 8, and also 12?

The LCM the 3, 8, and also 12 is 24. To find the LCM (least common multiple) the 3, 8, and also 12, we require to uncover the multiples that 3, 8, and also 12 (multiples of 3 = 3, 6, 9, 12 . . . . 24 . . . . ; multiples the 8 = 8, 16, 24, 32 . . . .; multiples of 12 = 12, 24, 36, 48 . . . .) and choose the the smallest multiple the is exactly divisible through 3, 8, and also 12, i.e., 24.

What is the Relation between GCF and LCM of 3, 8, 12?

The following equation can be supplied to refer the relation between GCF and LCM the 3, 8, 12, i.e. LCM(3, 8, 12) = <(3 × 8 × 12) × GCF(3, 8, 12)>/.

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What is the least Perfect Square Divisible by 3, 8, and also 12?

The the very least number divisible by 3, 8, and 12 = LCM(3, 8, 12)LCM that 3, 8, and also 12 = 2 × 2 × 2 × 3 ⇒ the very least perfect square divisible by each 3, 8, and also 12 = LCM(3, 8, 12) × 2 × 3 = 144 Therefore, 144 is the required number.

What space the methods to discover LCM that 3, 8, 12?

The commonly used techniques to discover the LCM of 3, 8, 12 are: