LCM that 9, 12, and 18 is the smallest number among all common multiples the 9, 12, and also 18. The first couple of multiples that 9, 12, and 18 room (9, 18, 27, 36, 45 . . .), (12, 24, 36, 48, 60 . . .), and (18, 36, 54, 72, 90 . . .) respectively. There space 3 frequently used techniques to find LCM the 9, 12, 18 - through listing multiples, by prime factorization, and also by department method.

You are watching: What is the least common multiple of 9 12 and 18

1.LCM the 9, 12, and 18
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM the 9, 12, and 18 is 36.

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Explanation:

The LCM of 3 non-zero integers, a(9), b(12), and c(18), is the smallest confident integer m(36) that is divisible by a(9), b(12), and c(18) without any kind of remainder.


The techniques to uncover the LCM that 9, 12, and also 18 are described below.

By prime Factorization MethodBy Listing MultiplesBy division Method

LCM the 9, 12, and also 18 by prime Factorization

Prime factorization of 9, 12, and also 18 is (3 × 3) = 32, (2 × 2 × 3) = 22 × 31, and (2 × 3 × 3) = 21 × 32 respectively. LCM that 9, 12, and 18 deserve to be acquired by multiply prime determinants raised to your respective greatest power, i.e. 22 × 32 = 36.Hence, the LCM of 9, 12, and 18 by prime factorization is 36.

LCM that 9, 12, and also 18 by Listing Multiples

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To calculate the LCM of 9, 12, 18 by listing out the typical multiples, we can follow the given listed below steps:

Step 1: list a couple of multiples of 9 (9, 18, 27, 36, 45 . . .), 12 (12, 24, 36, 48, 60 . . .), and also 18 (18, 36, 54, 72, 90 . . .).Step 2: The common multiples indigenous the multiples of 9, 12, and also 18 room 36, 72, . . .Step 3: The smallest common multiple the 9, 12, and 18 is 36.

∴ The least typical multiple the 9, 12, and also 18 = 36.

LCM the 9, 12, and also 18 by division Method

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To calculation the LCM that 9, 12, and also 18 by the department method, we will divide the numbers(9, 12, 18) by your prime determinants (preferably common). The product of this divisors provides the LCM the 9, 12, and also 18.

Step 2: If any of the given numbers (9, 12, 18) is a multiple of 2, division it by 2 and also write the quotient listed below it. Lug down any number the is no divisible by the element number.Step 3: proceed the measures until only 1s room left in the critical row.

The LCM the 9, 12, and also 18 is the product of every prime number on the left, i.e. LCM(9, 12, 18) by division method = 2 × 2 × 3 × 3 = 36.

☛ also Check:


Example 1: Verify the relationship in between the GCD and LCM that 9, 12, and 18.

Solution:

The relation in between GCD and LCM of 9, 12, and also 18 is given as,LCM(9, 12, 18) = <(9 × 12 × 18) × GCD(9, 12, 18)>/⇒ element factorization of 9, 12 and also 18:

9 = 3212 = 22 × 3118 = 21 × 32

∴ GCD that (9, 12), (12, 18), (9, 18) and (9, 12, 18) = 3, 6, 9 and also 3 respectively.Now, LHS = LCM(9, 12, 18) = 36.And, RHS = <(9 × 12 × 18) × GCD(9, 12, 18)>/ = <(1944) × 3>/<3 × 6 × 9> = 36LHS = RHS = 36.Hence verified.


Example 2: calculation the LCM the 9, 12, and also 18 utilizing the GCD the the given numbers.

Solution:

Prime administrate of 9, 12, 18:

9 = 3212 = 22 × 3118 = 21 × 32

Therefore, GCD(9, 12) = 3, GCD(12, 18) = 6, GCD(9, 18) = 9, GCD(9, 12, 18) = 3We know,LCM(9, 12, 18) = <(9 × 12 × 18) × GCD(9, 12, 18)>/LCM(9, 12, 18) = (1944 × 3)/(3 × 6 × 9) = 36⇒LCM(9, 12, 18) = 36


Example 3: find the the smallest number that is divisible through 9, 12, 18 exactly.

Solution:

The the smallest number that is divisible by 9, 12, and also 18 specifically is your LCM.⇒ Multiples the 9, 12, and 18:

Multiples the 9 = 9, 18, 27, 36, 45, 54, . . . .Multiples the 12 = 12, 24, 36, 48, 60, 72, . . . .Multiples the 18 = 18, 36, 54, 72, 90, 108, . . . .

Therefore, the LCM of 9, 12, and 18 is 36.


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FAQs on LCM of 9, 12, and 18

What is the LCM the 9, 12, and 18?

The LCM that 9, 12, and 18 is 36. To uncover the least common multiple that 9, 12, and also 18, we require to find the multiples of 9, 12, and also 18 (multiples of 9 = 9, 18, 27 . . . .; multiples the 12 = 12, 24, 36 . . . .; multiples of 18 = 18, 36, 54 . . . .) and also choose the the smallest multiple that is specifically divisible by 9, 12, and 18, i.e., 36.

What is the the very least Perfect Square Divisible by 9, 12, and also 18?

The the very least number divisible by 9, 12, and 18 = LCM(9, 12, 18)LCM of 9, 12, and also 18 = 2 × 2 × 3 × 3 ⇒ least perfect square divisible by each 9, 12, and also 18 = LCM(9, 12, 18) = 36 Therefore, 36 is the forced number.

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What are the approaches to uncover LCM the 9, 12, 18?

The generally used techniques to uncover the LCM that 9, 12, 18 are:

Listing MultiplesPrime administer MethodDivision Method

Which the the complying with is the LCM the 9, 12, and 18? 11, 96, 36, 110

The worth of LCM of 9, 12, 18 is the smallest typical multiple of 9, 12, and 18. The number to solve the given problem is 36.