LCM of 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 also 15 are (9, 18, 27, 36, 45 . . .), (12, 24, 36, 48, 60 . . .), and also (15, 30, 45, 60, 75 . . .) respectively. There space 3 commonly used techniques to uncover LCM that 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 of 9, 12, and 15 is 180.

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Explanation:

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


The techniques to find the LCM that 9, 12, and also 15 are explained below.

By department MethodBy Listing MultiplesBy prime Factorization Method

LCM the 9, 12, and 15 by department Method

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To calculate the LCM the 9, 12, and also 15 by the department method, we will divide the numbers(9, 12, 15) by their prime determinants (preferably common). The product of this divisors provides the LCM that 9, 12, and 15.

Step 2: If any type of of the offered numbers (9, 12, 15) is a lot of of 2, divide it through 2 and write the quotient below it. Lug down any kind 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 the 9, 12, and 15 is the product of every prime number on the left, i.e. LCM(9, 12, 15) by division method = 2 × 2 × 3 × 3 × 5 = 180.

LCM the 9, 12, and also 15 by Listing Multiples

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

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

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

LCM the 9, 12, and 15 by prime Factorization

Prime factorization of 9, 12, and 15 is (3 × 3) = 32, (2 × 2 × 3) = 22 × 31, and (3 × 5) = 31 × 51 respectively. LCM of 9, 12, and 15 have the right to be derived by multiply prime components raised to your respective greatest power, i.e. 22 × 32 × 51 = 180.Hence, the LCM of 9, 12, and also 15 by prime factorization is 180.

☛ additionally Check:


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

Solution:

The worth of LCM(9, 12, 15) will be the smallest number the is exactly divisible by 9, 12, and also 15.⇒ Multiples the 9, 12, and 15:

Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 153, 162, 171, 180, . . . .Multiples the 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 the 9, 12, and also 15 is 180.


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

Solution:

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

9 = 3212 = 22 × 3115 = 31 × 51

∴ GCD that (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: calculation the LCM of 9, 12, and also 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 that 9, 12, and also 15

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

The LCM that 9, 12, and also 15 is 180. To discover the LCM of 9, 12, and 15, we need to discover the multiples that 9, 12, and also 15 (multiples that 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 that is exactly divisible by 9, 12, and 15, i.e., 180.

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

To find the LCM that 9, 12, and 15 making use of prime factorization, us will discover the prime factors, (9 = 32), (12 = 22 × 31), and (15 = 31 × 51). LCM the 9, 12, and also 15 is the product the prime components raised to their respective greatest exponent among the number 9, 12, and also 15.⇒ LCM the 9, 12, 15 = 22 × 32 × 51 = 180.

Which of the complying with is the LCM that 9, 12, and 15? 96, 25, 50, 180

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

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

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