LCM that 9, 12, and also 15 is the smallest number amongst all typical multiples that 9, 12, and 15. The first couple of multiples that 9, 12, and 15 space (9, 18, 27, 36, 45 . . .), (12, 24, 36, 48, 60 . . .), and also (15, 30, 45, 60, 75 . . .) respectively. There space 3 frequently used techniques to discover LCM of 9, 12, 15 - by department method, through listing multiples, and also by prime factorization.

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

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

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Explanation:

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


The methods to find the LCM of 9, 12, and also 15 are defined below.

By division MethodBy Listing MultiplesBy element Factorization Method

LCM that 9, 12, and also 15 by division Method

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To calculate the LCM that 9, 12, and 15 through the division method, we will divide the numbers(9, 12, 15) by their prime components (preferably common). The product of this divisors offers the LCM that 9, 12, and 15.

Step 2: If any of the offered numbers (9, 12, 15) is a multiple of 2, divide it by 2 and write the quotient listed below it. Carry down any type of number that is no divisible by the prime number.Step 3: proceed the steps until only 1s room left in the critical row.

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

LCM that 9, 12, and also 15 through Listing Multiples

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

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

∴ The least common multiple that 9, 12, and also 15 = 180.

LCM of 9, 12, and 15 by element Factorization

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

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Example 1: uncover the the smallest number that is divisible by 9, 12, 15 exactly.

Solution:

The worth of LCM(9, 12, 15) will certainly be the smallest number that is specifically divisible by 9, 12, and 15.⇒ Multiples that 9, 12, and 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 the 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, . . . ., 135, 150, 165, 180, . . . .

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


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

Solution:

The relation between GCD and LCM the 9, 12, and 15 is provided as,LCM(9, 12, 15) = <(9 × 12 × 15) × GCD(9, 12, 15)>/⇒ prime factorization the 9, 12 and 15:

9 = 3212 = 22 × 3115 = 31 × 51

∴ GCD the (9, 12), (12, 15), (9, 15) and also (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 of 9, 12, and also 15 using the GCD the the provided numbers.

Solution:

Prime administer 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 top top LCM of 9, 12, and also 15

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

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

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

To discover the LCM the 9, 12, and 15 utilizing prime factorization, us will discover the prime factors, (9 = 32), (12 = 22 × 31), and also (15 = 31 × 51). LCM of 9, 12, and 15 is the product of prime factors raised to your respective highest exponent amongst the numbers 9, 12, and also 15.⇒ LCM that 9, 12, 15 = 22 × 32 × 51 = 180.

Which the the following is the LCM the 9, 12, and 15? 96, 25, 50, 180

The value of LCM the 9, 12, 15 is the smallest typical multiple the 9, 12, and 15. The number to solve the given condition is 180.

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What is the Relation in between GCF and LCM that 9, 12, 15?

The complying with equation can be supplied to express the relation in between GCF and LCM the 9, 12, 15, i.e. LCM(9, 12, 15) = <(9 × 12 × 15) × GCF(9, 12, 15)>/.