LCM of 8, 12, and also 16 is the the smallest number amongst all typical multiples of 8, 12, and 16. The first couple of multiples of 8, 12, and 16 room (8, 16, 24, 32, 40 . . .), (12, 24, 36, 48, 60 . . .), and also (16, 32, 48, 64, 80 . . .) respectively. There space 3 commonly used approaches to uncover LCM the 8, 12, 16 - through listing multiples, by division method, and also by element factorization.

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

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

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Explanation:

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


The techniques to find the LCM the 8, 12, and 16 are described below.

By department MethodBy Listing MultiplesBy prime Factorization Method

LCM the 8, 12, and 16 by division Method

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To calculate the LCM the 8, 12, and also 16 through the division 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 offered numbers (8, 12, 16) is a lot of of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible through the prime number.Step 3: continue the procedures until just 1s space left in the last row.

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

LCM of 8, 12, and 16 by Listing Multiples

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To calculation the LCM of 8, 12, 16 through listing out the typical multiples, we deserve to 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 also 16 (16, 32, 48, 64, 80 . . .).Step 2: The usual multiples indigenous the multiples that 8, 12, and also 16 are 48, 96, . . .Step 3: The smallest typical multiple that 8, 12, and also 16 is 48.

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

LCM that 8, 12, and 16 by prime Factorization

Prime administrate 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 have the right to be derived by multiplying prime components raised to your respective highest power, i.e. 24 × 31 = 48.Hence, the LCM that 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 of 8, 12, and also 16.

Solution:

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

8 = 2312 = 22 × 3116 = 24

∴ GCD the (8, 12), (12, 16), (8, 16) and (8, 12, 16) = 4, 4, 8 and also 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 the smallest number that is divisible by 8, 12, 16 exactly.

Solution:

The smallest number the is divisible through 8, 12, and 16 precisely is your LCM.⇒ Multiples of 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 the 8, 12, and 16 is 48.


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

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

The LCM the 8, 12, and also 16 is 48. To discover the least common multiple (LCM) that 8, 12, and also 16, we require to find 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 the smallest multiple that is exactly divisible by 8, 12, and also 16, i.e., 48.

Which of the complying with is the LCM of 8, 12, and 16? 11, 81, 48, 36

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

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

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

See more: What Is The Greatest Common Factor Of 3 And 6 ? Common Factors Of 3 And 6

How to find the LCM of 8, 12, and 16 by element Factorization?

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