LCM the 9, 12, and 15 is the smallest number amongst all common multiples that 9, 12, and 15. The first few multiples that 9, 12, and 15 room (9, 18, 27, 36, 45 . . .), (12, 24, 36, 48, 60 . . .), and (15, 30, 45, 60, 75 . . .) respectively. There space 3 frequently used approaches to uncover LCM the 9, 12, 15 - by department method, by listing multiples, and by prime factorization.

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1.LCM of 9, 12, and also 15
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM the 9, 12, and 15 is 180.

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Explanation:

The LCM of 3 non-zero integers, a(9), b(12), and c(15), is the smallest optimistic integer m(180) that is divisible by a(9), b(12), and also c(15) without any kind of remainder.


The techniques to discover the LCM the 9, 12, and 15 are described below.

By division MethodBy Listing MultiplesBy prime Factorization Method

LCM the 9, 12, and also 15 by department Method

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To calculate the LCM of 9, 12, and also 15 by the department method, we will certainly divide the numbers(9, 12, 15) by your prime components (preferably common). The product of these divisors gives the LCM that 9, 12, and also 15.

Step 2: If any kind of of the provided numbers (9, 12, 15) is a multiple of 2, division it by 2 and also write the quotient listed below it. Lug down any number that is no divisible by the prime number.Step 3: continue the actions until just 1s are left in the critical row.

The LCM that 9, 12, and also 15 is the product of every prime number on the left, i.e. LCM(9, 12, 15) by department method = 2 × 2 × 3 × 3 × 5 = 180.

LCM that 9, 12, and 15 by Listing Multiples

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To calculation the LCM that 9, 12, 15 by listing the end the usual multiples, we deserve to follow the given below steps:

Step 1: perform a couple of multiples of 9 (9, 18, 27, 36, 45 . . .), 12 (12, 24, 36, 48, 60 . . .), and also 15 (15, 30, 45, 60, 75 . . .).Step 2: The usual multiples indigenous the multiples that 9, 12, and also 15 are 180, 360, . . .Step 3: The smallest usual multiple of 9, 12, and 15 is 180.

∴ The least typical multiple the 9, 12, and also 15 = 180.

LCM of 9, 12, and also 15 by element Factorization

Prime administrate of 9, 12, and also 15 is (3 × 3) = 32, (2 × 2 × 3) = 22 × 31, and (3 × 5) = 31 × 51 respectively. LCM that 9, 12, and also 15 deserve to be obtained by multiply prime components raised to their respective highest power, i.e. 22 × 32 × 51 = 180.Hence, the LCM of 9, 12, and 15 by prime factorization is 180.

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Example 1: find the smallest number that is divisible through 9, 12, 15 exactly.

Solution:

The worth of LCM(9, 12, 15) will certainly be the the smallest number that is specifically divisible through 9, 12, and 15.⇒ Multiples that 9, 12, and also 15:

Multiples the 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 153, 162, 171, 180, . . . .Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 156, 168, 180, . . . .Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, . . . ., 135, 150, 165, 180, . . . .

Therefore, the LCM that 9, 12, and 15 is 180.


Example 2: Verify the relationship between the GCD and LCM of 9, 12, and also 15.

Solution:

The relation between GCD and LCM of 9, 12, and also 15 is offered as,LCM(9, 12, 15) = <(9 × 12 × 15) × GCD(9, 12, 15)>/⇒ element factorization of 9, 12 and 15:

9 = 3212 = 22 × 3115 = 31 × 51

∴ GCD of (9, 12), (12, 15), (9, 15) and (9, 12, 15) = 3, 3, 3 and also 3 respectively.Now, LHS = LCM(9, 12, 15) = 180.And, RHS = <(9 × 12 × 15) × GCD(9, 12, 15)>/ = <(1620) × 3>/<3 × 3 × 3> = 180LHS = RHS = 180.Hence verified.


Example 3: calculate the LCM that 9, 12, and 15 using the GCD of the provided numbers.

Solution:

Prime administrate of 9, 12, 15:

9 = 3212 = 22 × 3115 = 31 × 51

Therefore, GCD(9, 12) = 3, GCD(12, 15) = 3, GCD(9, 15) = 3, GCD(9, 12, 15) = 3We know,LCM(9, 12, 15) = <(9 × 12 × 15) × GCD(9, 12, 15)>/LCM(9, 12, 15) = (1620 × 3)/(3 × 3 × 3) = 180⇒LCM(9, 12, 15) = 180


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FAQs on LCM the 9, 12, and 15

What is the LCM the 9, 12, and 15?

The LCM of 9, 12, and 15 is 180. To find the LCM the 9, 12, and 15, we require to uncover the multiples the 9, 12, and 15 (multiples that 9 = 9, 18, 27, 36 . . . . 180 . . . . ; multiples that 12 = 12, 24, 36, 48 . . . . 180 . . . . ; multiples the 15 = 15, 30, 45, 60 . . . . 180 . . . . ) and also choose the smallest multiple that is precisely divisible by 9, 12, and 15, i.e., 180.

How to discover the LCM the 9, 12, and 15 by prime Factorization?

To find the LCM of 9, 12, and also 15 making use of prime factorization, we will uncover the element factors, (9 = 32), (12 = 22 × 31), and (15 = 31 × 51). LCM the 9, 12, and also 15 is the product of prime factors raised to your respective highest exponent among the number 9, 12, and also 15.⇒ LCM of 9, 12, 15 = 22 × 32 × 51 = 180.

Which of the adhering to is the LCM the 9, 12, and 15? 96, 25, 50, 180

The worth of LCM that 9, 12, 15 is the smallest usual multiple of 9, 12, and also 15. The number to solve the given condition is 180.

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What is the Relation between GCF and also LCM of 9, 12, 15?

The following equation can be used to express the relation between GCF and also LCM that 9, 12, 15, i.e. LCM(9, 12, 15) = <(9 × 12 × 15) × GCF(9, 12, 15)>/.