LCM of 12, 15, and also 18 is the smallest number among all common multiples that 12, 15, and also 18. The first few multiples of 12, 15, and also 18 room (12, 24, 36, 48, 60 . . .), (15, 30, 45, 60, 75 . . .), and also (18, 36, 54, 72, 90 . . .) respectively. There are 3 generally used approaches to uncover LCM that 12, 15, 18 - through listing multiples, by department method, and also by prime factorization.

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1.LCM of 12, 15, and also 18
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 12, 15, and also 18 is 180.

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Explanation:

The LCM of 3 non-zero integers, a(12), b(15), and also c(18), is the smallest positive integer m(180) the is divisible by a(12), b(15), and c(18) without any kind of remainder.


The methods to uncover the LCM the 12, 15, and also 18 are explained below.

By department MethodBy prime Factorization MethodBy Listing Multiples

LCM of 12, 15, and 18 by department Method

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To calculation the LCM of 12, 15, and also 18 through the department method, we will certainly divide the numbers(12, 15, 18) by your prime factors (preferably common). The product of this divisors offers the LCM of 12, 15, and 18.

Step 2: If any kind of of the offered numbers (12, 15, 18) is a lot of of 2, division it by 2 and also write the quotient below it. Carry down any number the is not divisible by the element number.Step 3: continue the measures until just 1s space left in the critical row.

The LCM of 12, 15, and also 18 is the product of all prime number on the left, i.e. LCM(12, 15, 18) by division method = 2 × 2 × 3 × 3 × 5 = 180.

LCM of 12, 15, and also 18 by prime Factorization

Prime administer of 12, 15, and 18 is (2 × 2 × 3) = 22 × 31, (3 × 5) = 31 × 51, and (2 × 3 × 3) = 21 × 32 respectively. LCM of 12, 15, and 18 have the right to be obtained by multiply prime determinants raised to your respective greatest power, i.e. 22 × 32 × 51 = 180.Hence, the LCM the 12, 15, and 18 by prime factorization is 180.

LCM the 12, 15, and also 18 through Listing Multiples

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To calculate the LCM the 12, 15, 18 by listing out the common multiples, we deserve to follow the given below steps:

Step 1: perform a couple of multiples the 12 (12, 24, 36, 48, 60 . . .), 15 (15, 30, 45, 60, 75 . . .), and 18 (18, 36, 54, 72, 90 . . .).Step 2: The common multiples from the multiples of 12, 15, and also 18 space 180, 360, . . .Step 3: The smallest typical multiple the 12, 15, and also 18 is 180.

∴ The least usual multiple the 12, 15, and also 18 = 180.

☛ also Check:


Example 3: Verify the relationship in between the GCD and LCM the 12, 15, and 18.

Solution:

The relation between GCD and LCM the 12, 15, and 18 is offered as,LCM(12, 15, 18) = <(12 × 15 × 18) × GCD(12, 15, 18)>/⇒ element factorization of 12, 15 and 18:

12 = 22 × 3115 = 31 × 5118 = 21 × 32

∴ GCD of (12, 15), (15, 18), (12, 18) and also (12, 15, 18) = 3, 3, 6 and also 3 respectively.Now, LHS = LCM(12, 15, 18) = 180.And, RHS = <(12 × 15 × 18) × GCD(12, 15, 18)>/ = <(3240) × 3>/<3 × 3 × 6> = 180LHS = RHS = 180.Hence verified.


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FAQs ~ above LCM of 12, 15, and also 18

What is the LCM the 12, 15, and 18?

The LCM that 12, 15, and 18 is 180. To discover the LCM (least typical multiple) the 12, 15, and also 18, we require to uncover the multiples that 12, 15, and also 18 (multiples the 12 = 12, 24, 36, 48 . . . . 180 . . . . ; multiples the 15 = 15, 30, 45, 60 . . . . 180 . . . . ; multiples the 18 = 18, 36, 54, 72 . . . . 180 . . . . ) and choose the the smallest multiple the is exactly divisible through 12, 15, and 18, i.e., 180.

How to discover the LCM of 12, 15, and also 18 by prime Factorization?

To discover the LCM the 12, 15, and 18 using prime factorization, us will find the element factors, (12 = 22 × 31), (15 = 31 × 51), and also (18 = 21 × 32). LCM the 12, 15, and also 18 is the product of prime determinants raised to your respective highest exponent amongst the number 12, 15, and also 18.⇒ LCM the 12, 15, 18 = 22 × 32 × 51 = 180.

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What are the techniques to discover LCM of 12, 15, 18?

The frequently used techniques to find the LCM of 12, 15, 18 are:

Prime administer MethodDivision MethodListing Multiples

What is the Relation in between GCF and also LCM the 12, 15, 18?

The complying with equation deserve to be offered to refer the relation between GCF and also LCM the 12, 15, 18, i.e. LCM(12, 15, 18) = <(12 × 15 × 18) × GCF(12, 15, 18)>/.