LCM of 4, 8, and also 16 is the the smallest number among all usual multiples the 4, 8, and 16. The first couple of multiples that 4, 8, and 16 space (4, 8, 12, 16, 20 . . .), (8, 16, 24, 32, 40 . . .), and (16, 32, 48, 64, 80 . . .) respectively. There are 3 generally used approaches to uncover LCM of 4, 8, 16 - by division method, by prime factorization, and also by listing multiples.

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

Answer: LCM of 4, 8, and also 16 is 16.

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Explanation:

The LCM of three non-zero integers, a(4), b(8), and c(16), is the smallest confident integer m(16) the is divisible by a(4), b(8), and c(16) without any remainder.


Let's look in ~ the various methods because that finding the LCM the 4, 8, and also 16.

By division MethodBy Listing MultiplesBy prime Factorization Method

LCM of 4, 8, and 16 by division Method

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To calculation the LCM that 4, 8, and also 16 by the division method, we will divide the numbers(4, 8, 16) by their prime components (preferably common). The product of this divisors offers the LCM of 4, 8, and also 16.

Step 2: If any of the offered numbers (4, 8, 16) is a many of 2, divide it by 2 and write the quotient below it. Lug down any kind of number that is not divisible by the element number.Step 3: proceed the actions until only 1s room left in the critical row.

The LCM that 4, 8, and also 16 is the product of all prime numbers on the left, i.e. LCM(4, 8, 16) by department method = 2 × 2 × 2 × 2 = 16.

LCM the 4, 8, and 16 by Listing Multiples

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To calculate the LCM of 4, 8, 16 by listing out the typical multiples, we have the right to follow the given below steps:

Step 1: perform a couple of multiples that 4 (4, 8, 12, 16, 20 . . .), 8 (8, 16, 24, 32, 40 . . .), and also 16 (16, 32, 48, 64, 80 . . .).Step 2: The typical multiples native the multiples that 4, 8, and 16 room 16, 32, . . .Step 3: The smallest common multiple that 4, 8, and 16 is 16.

∴ The least common multiple the 4, 8, and also 16 = 16.

LCM of 4, 8, and also 16 by element Factorization

Prime administer of 4, 8, and 16 is (2 × 2) = 22, (2 × 2 × 2) = 23, and (2 × 2 × 2 × 2) = 24 respectively. LCM of 4, 8, and 16 can be obtained by multiply prime components raised to your respective highest power, i.e. 24 = 16.Hence, the LCM that 4, 8, and also 16 by element factorization is 16.

☛ likewise Check:


Example 1: Verify the relationship between the GCD and also LCM the 4, 8, and 16.

Solution:

The relation in between GCD and LCM that 4, 8, and 16 is provided as,LCM(4, 8, 16) = <(4 × 8 × 16) × GCD(4, 8, 16)>/⇒ prime factorization the 4, 8 and 16:

4 = 228 = 2316 = 24

∴ GCD the (4, 8), (8, 16), (4, 16) and also (4, 8, 16) = 4, 8, 4 and also 4 respectively.Now, LHS = LCM(4, 8, 16) = 16.And, RHS = <(4 × 8 × 16) × GCD(4, 8, 16)>/ = <(512) × 4>/<4 × 8 × 4> = 16LHS = RHS = 16.Hence verified.


Example 2: find the the smallest number that is divisible through 4, 8, 16 exactly.

Solution:

The the smallest number that is divisible by 4, 8, and 16 exactly is their LCM.⇒ Multiples of 4, 8, and also 16:

Multiples the 4 = 4, 8, 12, 16, 20, 24, 28, . . . .Multiples the 8 = 8, 16, 24, 32, 40, 48, 56, . . . .Multiples that 16 = 16, 32, 48, 64, 80, 96, 112, . . . .

Therefore, the LCM of 4, 8, and also 16 is 16.


Example 3: calculate the LCM of 4, 8, and 16 making use of the GCD of the given numbers.

Solution:

Prime administer of 4, 8, 16:

4 = 228 = 2316 = 24

Therefore, GCD(4, 8) = 4, GCD(8, 16) = 8, GCD(4, 16) = 4, GCD(4, 8, 16) = 4We know,LCM(4, 8, 16) = <(4 × 8 × 16) × GCD(4, 8, 16)>/LCM(4, 8, 16) = (512 × 4)/(4 × 8 × 4) = 16⇒LCM(4, 8, 16) = 16


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FAQs top top LCM that 4, 8, and also 16

What is the LCM of 4, 8, and 16?

The LCM of 4, 8, and 16 is 16. To uncover the LCM (least common multiple) the 4, 8, and 16, we need to uncover the multiples the 4, 8, and 16 (multiples of 4 = 4, 8, 12 . . . .; multiples the 8 = 8, 16, 24 . . . .; multiples of 16 = 16, 32, 48 . . . .) and also choose the the smallest multiple the is specifically divisible by 4, 8, and 16, i.e., 16.

What is the least Perfect Square Divisible through 4, 8, and 16?

The least number divisible by 4, 8, and 16 = LCM(4, 8, 16)LCM the 4, 8, and also 16 = 2 × 2 × 2 × 2 ⇒ least perfect square divisible by each 4, 8, and also 16 = LCM(4, 8, 16) = 16 Therefore, 16 is the compelled number.

What is the Relation in between GCF and LCM of 4, 8, 16?

The following equation deserve to be offered to express the relation between GCF and also LCM the 4, 8, 16, i.e. LCM(4, 8, 16) = <(4 × 8 × 16) × GCF(4, 8, 16)>/.

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Which the the complying with is the LCM of 4, 8, and also 16? 5, 105, 16, 2

The value of LCM that 4, 8, 16 is the smallest usual multiple of 4, 8, and 16. The number solve the given problem is 16.