LCM that 8, 12, and also 16 is the the smallest number amongst all common multiples the 8, 12, and 16. The first few multiples that 8, 12, and 16 space (8, 16, 24, 32, 40 . . .), (12, 24, 36, 48, 60 . . .), and (16, 32, 48, 64, 80 . . .) respectively. There are 3 typically used methods to uncover LCM of 8, 12, 16 - by listing multiples, by division method, and also by element factorization.

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

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

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Explanation:

The LCM of 3 non-zero integers, a(8), b(12), and also c(16), is the smallest optimistic integer m(48) the is divisible by a(8), b(12), and c(16) without any kind of remainder.


The techniques to uncover the LCM of 8, 12, and also 16 are defined below.

By division MethodBy Listing MultiplesBy prime Factorization Method

LCM of 8, 12, and 16 by division Method

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

Step 2: If any kind of of the given numbers (8, 12, 16) is a multiple of 2, divide it by 2 and also write the quotient listed below it. Bring down any type of number that is not divisible by the element number.Step 3: proceed the measures until just 1s are left in the critical row.

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

LCM the 8, 12, and also 16 by Listing Multiples

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To calculation the LCM that 8, 12, 16 by listing out the typical multiples, we have the right to follow the given listed below steps:

Step 1: list a few multiples of 8 (8, 16, 24, 32, 40 . . .), 12 (12, 24, 36, 48, 60 . . .), and 16 (16, 32, 48, 64, 80 . . .).Step 2: The common multiples indigenous the multiples the 8, 12, and 16 room 48, 96, . . .Step 3: The smallest usual multiple of 8, 12, and 16 is 48.

∴ The least common multiple the 8, 12, and also 16 = 48.

LCM the 8, 12, and 16 by prime Factorization

Prime administer of 8, 12, and also 16 is (2 × 2 × 2) = 23, (2 × 2 × 3) = 22 × 31, and (2 × 2 × 2 × 2) = 24 respectively. LCM that 8, 12, and also 16 can be obtained by multiply prime factors raised to their respective greatest power, i.e. 24 × 31 = 48.Hence, the LCM the 8, 12, and also 16 by element factorization is 48.

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

Solution:

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

8 = 2312 = 22 × 3116 = 24

∴ GCD that (8, 12), (12, 16), (8, 16) and (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: uncover the smallest number that is divisible by 8, 12, 16 exactly.

Solution:

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

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

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


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FAQs top top LCM that 8, 12, and also 16

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

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

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

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

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

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

See more: 15,000,000,000 - 15000000000 In Scientific Notation

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

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