LCM that 4, 7, and 8 is the smallest number among all typical multiples that 4, 7, and 8. The first few multiples that 4, 7, and 8 space (4, 8, 12, 16, 20 . . .), (7, 14, 21, 28, 35 . . .), and also (8, 16, 24, 32, 40 . . .) respectively. There space 3 frequently used techniques to uncover LCM that 4, 7, 8 - through listing multiples, by division method, and by element factorization.

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1.LCM of 4, 7, and also 8
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM the 4, 7, and 8 is 56.

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Explanation:

The LCM of 3 non-zero integers, a(4), b(7), and also c(8), is the smallest optimistic integer m(56) the is divisible by a(4), b(7), and c(8) without any kind of remainder.


The approaches to discover the LCM the 4, 7, and 8 are described below.

By division MethodBy element Factorization MethodBy Listing Multiples

LCM that 4, 7, and 8 by division Method

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To calculate the LCM that 4, 7, and also 8 by the division method, we will divide the numbers(4, 7, 8) by your prime determinants (preferably common). The product of these divisors offers the LCM that 4, 7, and also 8.

Step 2: If any kind of of the given numbers (4, 7, 8) is a multiple of 2, divide it by 2 and also write the quotient listed below it. Lug down any type of number the is not divisible through the prime number.Step 3: proceed the steps until only 1s are left in the critical row.

The LCM the 4, 7, and also 8 is the product of all prime number on the left, i.e. LCM(4, 7, 8) by department method = 2 × 2 × 2 × 7 = 56.

LCM the 4, 7, and also 8 by element Factorization

Prime factorization of 4, 7, and also 8 is (2 × 2) = 22, (7) = 71, and also (2 × 2 × 2) = 23 respectively. LCM of 4, 7, and 8 deserve to be acquired by multiply prime components raised to your respective highest possible power, i.e. 23 × 71 = 56.Hence, the LCM that 4, 7, and also 8 by element factorization is 56.

LCM the 4, 7, and also 8 by Listing Multiples

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To calculation the LCM of 4, 7, 8 by listing the end the typical multiples, we have the right to follow the given listed below steps:

Step 1: list a couple of multiples of 4 (4, 8, 12, 16, 20 . . .), 7 (7, 14, 21, 28, 35 . . .), and 8 (8, 16, 24, 32, 40 . . .).Step 2: The typical multiples indigenous the multiples of 4, 7, and also 8 room 56, 112, . . .Step 3: The smallest typical multiple that 4, 7, and also 8 is 56.

∴ The least typical multiple the 4, 7, and also 8 = 56.

☛ also Check:


Example 2: Verify the relationship in between the GCD and LCM of 4, 7, and also 8.

Solution:

The relation between GCD and LCM that 4, 7, and also 8 is provided as,LCM(4, 7, 8) = <(4 × 7 × 8) × GCD(4, 7, 8)>/⇒ element factorization the 4, 7 and 8:

4 = 227 = 718 = 23

∴ GCD that (4, 7), (7, 8), (4, 8) and (4, 7, 8) = 1, 1, 4 and 1 respectively.Now, LHS = LCM(4, 7, 8) = 56.And, RHS = <(4 × 7 × 8) × GCD(4, 7, 8)>/ = <(224) × 1>/<1 × 1 × 4> = 56LHS = RHS = 56.Hence verified.


Example 3: discover the smallest number that is divisible by 4, 7, 8 exactly.

Solution:

The the smallest number that is divisible through 4, 7, and 8 precisely is your LCM.⇒ Multiples that 4, 7, and also 8:

Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, . . . .Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, . . . .Multiples that 8 = 8, 16, 24, 32, 40, 48, 56, . . . .

Therefore, the LCM that 4, 7, and 8 is 56.


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FAQs ~ above LCM the 4, 7, and also 8

What is the LCM of 4, 7, and 8?

The LCM that 4, 7, and 8 is 56. To uncover the LCM of 4, 7, and also 8, we require to find the multiples the 4, 7, and 8 (multiples the 4 = 4, 8, 12, 16 . . . . 56 . . . . ; multiples of 7 = 7, 14, 21, 28 . . . . 56 . . . . ; multiples that 8 = 8, 16, 24, 32, 48, 56 . . . .) and choose the the smallest multiple that is specifically divisible by 4, 7, and 8, i.e., 56.

How to uncover the LCM of 4, 7, and also 8 by prime Factorization?

To uncover the LCM of 4, 7, and 8 making use of prime factorization, we will discover the prime factors, (4 = 22), (7 = 71), and (8 = 23). LCM of 4, 7, and 8 is the product the prime factors raised to your respective greatest exponent amongst the number 4, 7, and also 8.⇒ LCM of 4, 7, 8 = 23 × 71 = 56.

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What is the Relation between GCF and LCM of 4, 7, 8?

The following equation have the right to be provided to refer the relation in between GCF and also LCM that 4, 7, 8, i.e. LCM(4, 7, 8) = <(4 × 7 × 8) × GCF(4, 7, 8)>/.

What space the methods to discover LCM that 4, 7, 8?

The typically used techniques to discover the LCM that 4, 7, 8 are: