LCM the 4, 5, and 8 is the smallest number among all usual multiples of 4, 5, and 8. The first few multiples that 4, 5, and also 8 are (4, 8, 12, 16, 20 . . .), (5, 10, 15, 20, 25 . . .), and also (8, 16, 24, 32, 40 . . .) respectively. There space 3 commonly used techniques to uncover LCM of 4, 5, 8 - by department method, by listing multiples, and by element factorization.

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1.LCM of 4, 5, and 8
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM the 4, 5, and also 8 is 40.

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Explanation:

The LCM of 3 non-zero integers, a(4), b(5), and c(8), is the smallest positive integer m(40) the is divisible by a(4), b(5), and also c(8) without any kind of remainder.


The methods to uncover the LCM of 4, 5, and also 8 are defined below.

By department MethodBy prime Factorization MethodBy Listing Multiples

LCM the 4, 5, and 8 by division Method

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To calculate the LCM that 4, 5, and 8 by the department method, we will certainly divide the numbers(4, 5, 8) by their prime components (preferably common). The product of this divisors offers the LCM of 4, 5, and also 8.

Step 2: If any of the given numbers (4, 5, 8) is a many of 2, division it by 2 and write the quotient below it. Bring down any type of number that is no divisible through the element number.Step 3: continue the measures until only 1s room left in the critical row.

The LCM of 4, 5, and 8 is the product of all prime number on the left, i.e. LCM(4, 5, 8) by department method = 2 × 2 × 2 × 5 = 40.

LCM the 4, 5, and 8 by prime Factorization

Prime administer of 4, 5, and also 8 is (2 × 2) = 22, (5) = 51, and (2 × 2 × 2) = 23 respectively. LCM that 4, 5, and 8 deserve to be obtained by multiplying prime components raised to their respective highest power, i.e. 23 × 51 = 40.Hence, the LCM the 4, 5, and also 8 by prime factorization is 40.

LCM of 4, 5, and also 8 by Listing Multiples

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To calculate the LCM that 4, 5, 8 by listing the end the typical multiples, we have the right to follow the given listed below steps:

Step 1: perform a few multiples of 4 (4, 8, 12, 16, 20 . . .), 5 (5, 10, 15, 20, 25 . . .), and also 8 (8, 16, 24, 32, 40 . . .).Step 2: The common multiples native the multiples of 4, 5, and also 8 space 40, 80, . . .Step 3: The smallest common multiple the 4, 5, and also 8 is 40.

∴ The least typical multiple the 4, 5, and also 8 = 40.

☛ also Check:


Example 2: Verify the relationship between the GCD and also LCM that 4, 5, and also 8.

Solution:

The relation between GCD and LCM the 4, 5, and 8 is provided as,LCM(4, 5, 8) = <(4 × 5 × 8) × GCD(4, 5, 8)>/⇒ prime factorization the 4, 5 and also 8:

4 = 225 = 518 = 23

∴ GCD of (4, 5), (5, 8), (4, 8) and (4, 5, 8) = 1, 1, 4 and also 1 respectively.Now, LHS = LCM(4, 5, 8) = 40.And, RHS = <(4 × 5 × 8) × GCD(4, 5, 8)>/ = <(160) × 1>/<1 × 1 × 4> = 40LHS = RHS = 40.Hence verified.


Example 3: find the smallest number that is divisible through 4, 5, 8 exactly.

Solution:

The the smallest number that is divisible by 4, 5, and 8 precisely is your LCM.⇒ Multiples that 4, 5, and also 8:

Multiples that 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . .Multiples the 5 = 5, 10, 15, 20, 25, 30, 35, 40, . . . .Multiples that 8 = 8, 16, 24, 32, 40, . . . .

Therefore, the LCM of 4, 5, and 8 is 40.


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FAQs on LCM of 4, 5, and also 8

What is the LCM that 4, 5, and also 8?

The LCM of 4, 5, and 8 is 40. To uncover the least usual multiple of 4, 5, and also 8, we need to uncover the multiples of 4, 5, and also 8 (multiples the 4 = 4, 8, 12, 16 . . . . 40 . . . . ; multiples of 5 = 5, 10, 15, 20 . . . . 40 . . . . ; multiples of 8 = 8, 16, 24, 32 . . . . 40 . . . . ) and choose the the smallest multiple the is precisely divisible by 4, 5, and 8, i.e., 40.

What space the approaches to discover LCM that 4, 5, 8?

The typically used approaches to find the LCM of 4, 5, 8 are:

Prime factorization MethodDivision MethodListing Multiples

How to find the LCM of 4, 5, and 8 by prime Factorization?

To discover the LCM that 4, 5, and also 8 making use of prime factorization, we will uncover the element factors, (4 = 22), (5 = 51), and (8 = 23). LCM that 4, 5, and 8 is the product that prime components raised to their respective highest possible exponent among the numbers 4, 5, and 8.⇒ LCM of 4, 5, 8 = 23 × 51 = 40.

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Which that the complying with is the LCM of 4, 5, and also 8? 40, 81, 42, 24

The worth of LCM of 4, 5, 8 is the smallest typical multiple the 4, 5, and 8. The number solve the given problem is 40.