LCM that 8, 12, and also 16 is the the smallest number among all usual multiples of 8, 12, and also 16. The first couple of multiples that 8, 12, and 16 room (8, 16, 24, 32, 40 . . .), (12, 24, 36, 48, 60 . . .), and also (16, 32, 48, 64, 80 . . .) respectively. There room 3 generally used techniques to find LCM that 8, 12, 16 - by listing multiples, by department method, and also by element factorization.

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1.LCM the 8, 12, and 16
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM the 8, 12, and also 16 is 48.

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Explanation:

The LCM of three non-zero integers, a(8), b(12), and c(16), is the smallest optimistic integer m(48) that is divisible by a(8), b(12), and c(16) without any kind of remainder.


The approaches to find the LCM that 8, 12, and also 16 are described below.

By division MethodBy Listing MultiplesBy element Factorization Method

LCM that 8, 12, and 16 by division Method

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To calculate the LCM that 8, 12, and also 16 by the department method, we will certainly divide the numbers(8, 12, 16) by your prime determinants (preferably common). The product of these divisors provides the LCM that 8, 12, and 16.

Step 2: If any type of of the offered numbers (8, 12, 16) is a lot of of 2, division it by 2 and also 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 just 1s are left in the last row.

The LCM that 8, 12, and also 16 is the product of all prime numbers on the left, i.e. LCM(8, 12, 16) by division method = 2 × 2 × 2 × 2 × 3 = 48.

LCM the 8, 12, and 16 through Listing Multiples

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To calculate the LCM the 8, 12, 16 by listing the end the typical multiples, we can follow the given listed below steps:

Step 1: list a couple of multiples of 8 (8, 16, 24, 32, 40 . . .), 12 (12, 24, 36, 48, 60 . . .), and 16 (16, 32, 48, 64, 80 . . .).Step 2: The typical multiples from the multiples that 8, 12, and also 16 space 48, 96, . . .Step 3: The smallest typical multiple of 8, 12, and also 16 is 48.

∴ The least typical multiple that 8, 12, and also 16 = 48.

LCM the 8, 12, and 16 by element Factorization

Prime administrate of 8, 12, and 16 is (2 × 2 × 2) = 23, (2 × 2 × 3) = 22 × 31, and also (2 × 2 × 2 × 2) = 24 respectively. LCM that 8, 12, and also 16 have the right to be acquired by multiply prime determinants raised to their respective greatest power, i.e. 24 × 31 = 48.Hence, the LCM the 8, 12, and also 16 by prime factorization is 48.

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Example 2: Verify the relationship between the GCD and LCM that 8, 12, and 16.

Solution:

The relation between GCD and LCM of 8, 12, and also 16 is offered as,LCM(8, 12, 16) = <(8 × 12 × 16) × GCD(8, 12, 16)>/⇒ prime factorization the 8, 12 and also 16:

8 = 2312 = 22 × 3116 = 24

∴ GCD the (8, 12), (12, 16), (8, 16) and also (8, 12, 16) = 4, 4, 8 and 4 respectively.Now, LHS = LCM(8, 12, 16) = 48.And, RHS = <(8 × 12 × 16) × GCD(8, 12, 16)>/ = <(1536) × 4>/<4 × 4 × 8> = 48LHS = RHS = 48.Hence verified.


Example 3: discover the smallest number that is divisible by 8, 12, 16 exactly.

Solution:

The the smallest number that is divisible by 8, 12, and also 16 precisely is your LCM.⇒ Multiples that 8, 12, and 16:

Multiples that 8 = 8, 16, 24, 32, 40, 48, 56, . . . .Multiples the 12 = 12, 24, 36, 48, 60, 72, 84, . . . .Multiples the 16 = 16, 32, 48, 64, 80, 96, 112, . . . .

Therefore, the LCM that 8, 12, and also 16 is 48.


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FAQs ~ above LCM that 8, 12, and also 16

What is the LCM of 8, 12, and 16?

The LCM of 8, 12, and also 16 is 48. To discover the least typical multiple (LCM) that 8, 12, and 16, we require to discover the multiples the 8, 12, and 16 (multiples the 8 = 8, 16, 24, 32, 48 . . . .; multiples the 12 = 12, 24, 36, 48 . . . .; multiples of 16 = 16, 32, 48, 64 . . . .) and also choose the smallest multiple that is precisely divisible by 8, 12, and also 16, i.e., 48.

Which that the following is the LCM of 8, 12, and also 16? 11, 81, 48, 36

The value of LCM of 8, 12, 16 is the smallest common multiple that 8, 12, and also 16. The number to solve the given condition is 48.

What is the Relation between GCF and LCM that 8, 12, 16?

The adhering to equation can be provided to express the relation in between GCF and also LCM of 8, 12, 16, i.e. LCM(8, 12, 16) = <(8 × 12 × 16) × GCF(8, 12, 16)>/.

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How to discover the LCM of 8, 12, and also 16 by prime Factorization?

To discover the LCM of 8, 12, and also 16 using prime factorization, we will uncover the element factors, (8 = 23), (12 = 22 × 31), and also (16 = 24). LCM of 8, 12, and 16 is the product that prime factors raised to their respective highest possible exponent amongst the numbers 8, 12, and 16.⇒ LCM of 8, 12, 16 = 24 × 31 = 48.