LCM of 6, 7, and 8 is the smallest number among all typical multiples that 6, 7, and also 8. The first few multiples the 6, 7, and 8 are (6, 12, 18, 24, 30 . . .), (7, 14, 21, 28, 35 . . .), and (8, 16, 24, 32, 40 . . .) respectively. There room 3 commonly used techniques to discover LCM that 6, 7, 8 - by element factorization, by division method, and by listing multiples.

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1.LCM the 6, 7, and 8
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM of 6, 7, and 8 is 168.

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Explanation:

The LCM of 3 non-zero integers, a(6), b(7), and c(8), is the smallest hopeful integer m(168) that is divisible by a(6), b(7), and c(8) without any kind of remainder.


Let's look in ~ the various methods because that finding the LCM that 6, 7, and also 8.

By Listing MultiplesBy element Factorization MethodBy division Method

LCM the 6, 7, and 8 through Listing Multiples

To calculate the LCM that 6, 7, 8 by listing the end the typical multiples, we deserve to follow the given listed below steps:

Step 1: list a couple of multiples of 6 (6, 12, 18, 24, 30 . . .), 7 (7, 14, 21, 28, 35 . . .), and 8 (8, 16, 24, 32, 40 . . .).Step 2: The usual multiples indigenous the multiples that 6, 7, and also 8 room 168, 336, . . .Step 3: The smallest common multiple that 6, 7, and also 8 is 168.

∴ The least common multiple the 6, 7, and 8 = 168.

LCM that 6, 7, and also 8 by element Factorization

Prime administrate of 6, 7, and 8 is (2 × 3) = 21 × 31, (7) = 71, and also (2 × 2 × 2) = 23 respectively. LCM of 6, 7, and 8 can be derived by multiplying prime factors raised to their respective highest possible power, i.e. 23 × 31 × 71 = 168.Hence, the LCM of 6, 7, and 8 by prime factorization is 168.

LCM of 6, 7, and also 8 by department Method

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To calculation the LCM that 6, 7, and 8 through the department method, we will certainly divide the numbers(6, 7, 8) by their prime factors (preferably common). The product of this divisors gives the LCM of 6, 7, and also 8.

Step 2: If any kind of of the given numbers (6, 7, 8) is a multiple of 2, division it through 2 and also write the quotient listed below it. Lug down any kind of number the is no divisible by the prime number.Step 3: proceed the procedures until only 1s are left in the last row.

The LCM the 6, 7, and also 8 is the product of all prime number on the left, i.e. LCM(6, 7, 8) by department method = 2 × 2 × 2 × 3 × 7 = 168.

☛ likewise Check:


Example 1: uncover the smallest number the is divisible by 6, 7, 8 exactly.

Solution:

The value of LCM(6, 7, 8) will certainly be the the smallest number the is precisely divisible by 6, 7, and 8.⇒ Multiples of 6, 7, and 8:

Multiples the 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . ., 150, 156, 162, 168, . . . .Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 154, 161, 168, . . . .Multiples the 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . . ., 136, 144, 152, 160, 168, . . . .

Therefore, the LCM that 6, 7, and 8 is 168.


Example 2: Verify the relationship between the GCD and LCM that 6, 7, and also 8.

Solution:

The relation in between GCD and LCM that 6, 7, and also 8 is provided as,LCM(6, 7, 8) = <(6 × 7 × 8) × GCD(6, 7, 8)>/⇒ prime factorization the 6, 7 and also 8:

6 = 21 × 317 = 718 = 23

∴ GCD the (6, 7), (7, 8), (6, 8) and also (6, 7, 8) = 1, 1, 2 and 1 respectively.Now, LHS = LCM(6, 7, 8) = 168.And, RHS = <(6 × 7 × 8) × GCD(6, 7, 8)>/ = <(336) × 1>/<1 × 1 × 2> = 168LHS = RHS = 168.Hence verified.


Example 3: calculation the LCM that 6, 7, and 8 using the GCD of the provided numbers.

Solution:

Prime factorization of 6, 7, 8:

6 = 21 × 317 = 718 = 23

Therefore, GCD(6, 7) = 1, GCD(7, 8) = 1, GCD(6, 8) = 2, GCD(6, 7, 8) = 1We know,LCM(6, 7, 8) = <(6 × 7 × 8) × GCD(6, 7, 8)>/LCM(6, 7, 8) = (336 × 1)/(1 × 1 × 2) = 168⇒LCM(6, 7, 8) = 168


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FAQs top top LCM of 6, 7, and also 8

What is the LCM that 6, 7, and also 8?

The LCM of 6, 7, and also 8 is 168. To uncover the least usual multiple of 6, 7, and 8, we require to find the multiples the 6, 7, and also 8 (multiples of 6 = 6, 12, 18, 24 . . . . 168 . . . . ; multiples of 7 = 7, 14, 21, 28 . . . . 168 . . . . ; multiples that 8 = 8, 16, 24, 32 . . . . 168 . . . . ) and also choose the smallest multiple the is precisely divisible by 6, 7, and also 8, i.e., 168.

What is the Relation in between GCF and also LCM of 6, 7, 8?

The complying with equation deserve to be provided to refer the relation in between GCF and LCM the 6, 7, 8, i.e. LCM(6, 7, 8) = <(6 × 7 × 8) × GCF(6, 7, 8)>/.

How to find the LCM the 6, 7, and 8 by prime Factorization?

To discover the LCM that 6, 7, and 8 utilizing prime factorization, we will discover the element factors, (6 = 21 × 31), (7 = 71), and (8 = 23). LCM of 6, 7, and 8 is the product of prime determinants raised to your respective greatest exponent amongst the number 6, 7, and 8.⇒ LCM the 6, 7, 8 = 23 × 31 × 71 = 168.

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What is the least Perfect Square Divisible by 6, 7, and 8?

The the very least number divisible through 6, 7, and also 8 = LCM(6, 7, 8)LCM the 6, 7, and also 8 = 2 × 2 × 2 × 3 × 7 ⇒ least perfect square divisible by each 6, 7, and 8 = LCM(6, 7, 8) × 2 × 3 × 7 = 7056 Therefore, 7056 is the required number.