LCM that 6, 8, and 15 is the the smallest number amongst all typical multiples that 6, 8, and also 15. The first couple of multiples the 6, 8, and 15 space (6, 12, 18, 24, 30 . . .), (8, 16, 24, 32, 40 . . .), and (15, 30, 45, 60, 75 . . .) respectively. There room 3 commonly used approaches to uncover LCM the 6, 8, 15 - by department method, by element factorization, and also by listing multiples.

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1.LCM of 6, 8, and 15
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM that 6, 8, and also 15 is 120.

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Explanation:

The LCM of 3 non-zero integers, a(6), b(8), and c(15), is the smallest optimistic integer m(120) that is divisible through a(6), b(8), and also c(15) without any kind of remainder.


The approaches to discover the LCM that 6, 8, and 15 are described below.

By element Factorization MethodBy Listing MultiplesBy division Method

LCM the 6, 8, and also 15 by element Factorization

Prime administer of 6, 8, and also 15 is (2 × 3) = 21 × 31, (2 × 2 × 2) = 23, and also (3 × 5) = 31 × 51 respectively. LCM the 6, 8, and 15 deserve to be derived by multiplying prime determinants raised to your respective highest power, i.e. 23 × 31 × 51 = 120.Hence, the LCM of 6, 8, and 15 by prime factorization is 120.

LCM the 6, 8, and 15 by Listing Multiples

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To calculation the LCM of 6, 8, 15 by listing out the common multiples, we deserve to follow the given listed below steps:

Step 1: perform a few multiples of 6 (6, 12, 18, 24, 30 . . .), 8 (8, 16, 24, 32, 40 . . .), and also 15 (15, 30, 45, 60, 75 . . .).Step 2: The typical multiples from the multiples the 6, 8, and also 15 room 120, 240, . . .Step 3: The smallest typical multiple of 6, 8, and also 15 is 120.

∴ The least typical multiple the 6, 8, and also 15 = 120.

LCM of 6, 8, and also 15 by department Method

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To calculation the LCM that 6, 8, and 15 by the department method, we will certainly divide the numbers(6, 8, 15) by your prime determinants (preferably common). The product of these divisors offers the LCM of 6, 8, and also 15.

Step 2: If any type of of the offered numbers (6, 8, 15) is a lot of of 2, division it through 2 and write the quotient below it. Lug down any type of number the is no divisible by the element number.Step 3: continue the actions until only 1s room left in the last row.

The LCM that 6, 8, and 15 is the product of every prime numbers on the left, i.e. LCM(6, 8, 15) by department method = 2 × 2 × 2 × 3 × 5 = 120.

☛ likewise Check:


Example 1: Verify the relationship in between the GCD and also LCM the 6, 8, and also 15.

Solution:

The relation between GCD and also LCM that 6, 8, and 15 is offered as,LCM(6, 8, 15) = <(6 × 8 × 15) × GCD(6, 8, 15)>/⇒ prime factorization that 6, 8 and also 15:

6 = 21 × 318 = 2315 = 31 × 51

∴ GCD the (6, 8), (8, 15), (6, 15) and (6, 8, 15) = 2, 1, 3 and 1 respectively.Now, LHS = LCM(6, 8, 15) = 120.And, RHS = <(6 × 8 × 15) × GCD(6, 8, 15)>/ = <(720) × 1>/<2 × 1 × 3> = 120LHS = RHS = 120.Hence verified.


Example 2: calculation the LCM of 6, 8, and also 15 making use of the GCD that the offered numbers.

Solution:

Prime factorization of 6, 8, 15:

6 = 21 × 318 = 2315 = 31 × 51

Therefore, GCD(6, 8) = 2, GCD(8, 15) = 1, GCD(6, 15) = 3, GCD(6, 8, 15) = 1We know,LCM(6, 8, 15) = <(6 × 8 × 15) × GCD(6, 8, 15)>/LCM(6, 8, 15) = (720 × 1)/(2 × 1 × 3) = 120⇒LCM(6, 8, 15) = 120


Example 3: discover the smallest number the is divisible through 6, 8, 15 exactly.

Solution:

The value of LCM(6, 8, 15) will certainly be the the smallest number that is specifically divisible by 6, 8, and 15.⇒ Multiples the 6, 8, and 15:

Multiples the 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . ., 102, 108, 114, 120, . . . .Multiples the 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . . ., 104, 112, 120, . . . .Multiples that 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, . . . ., 75, 90, 105, 120, . . . .

Therefore, the LCM the 6, 8, and 15 is 120.


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FAQs top top LCM of 6, 8, and also 15

What is the LCM of 6, 8, and 15?

The LCM that 6, 8, and 15 is 120. To discover the least common multiple (LCM) of 6, 8, and 15, we require to discover the multiples the 6, 8, and 15 (multiples of 6 = 6, 12, 18, 24 . . . . 120 . . . . ; multiples of 8 = 8, 16, 24, 32 . . . . 120 . . . . ; multiples of 15 = 15, 30, 45, 60 . . . . 120 . . . . ) and also choose the smallest multiple the is precisely divisible by 6, 8, and also 15, i.e., 120.

What is the Relation in between GCF and also LCM the 6, 8, 15?

The complying with equation have the right to be used to express the relation between GCF and LCM the 6, 8, 15, i.e. LCM(6, 8, 15) = <(6 × 8 × 15) × GCF(6, 8, 15)>/.

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What are the methods to find LCM that 6, 8, 15?

The generally used approaches to find the LCM of 6, 8, 15 are:

Prime factorization MethodListing MultiplesDivision Method

Which the the following is the LCM of 6, 8, and also 15? 120, 100, 25, 12

The worth of LCM of 6, 8, 15 is the smallest usual multiple that 6, 8, and also 15. The number to solve the given problem is 120.