LCM that 12, 15, and also 18 is the smallest number amongst all usual multiples the 12, 15, and 18. The first few multiples that 12, 15, and also 18 are (12, 24, 36, 48, 60 . . .), (15, 30, 45, 60, 75 . . .), and also (18, 36, 54, 72, 90 . . .) respectively. There room 3 commonly used approaches to discover LCM the 12, 15, 18 - by listing multiples, by division method, and also by prime factorization.

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 1 LCM that 12, 15, and 18 2 List the Methods 3 Solved Examples 4 FAQs

Answer: LCM the 12, 15, and 18 is 180.

Explanation:

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

The methods to discover the LCM of 12, 15, and 18 are defined below.

By division MethodBy prime Factorization MethodBy Listing Multiples

### LCM of 12, 15, and also 18 by division Method

To calculate the LCM the 12, 15, and also 18 by the department method, we will certainly divide the numbers(12, 15, 18) by their prime factors (preferably common). The product of these divisors gives the LCM that 12, 15, and also 18.

Step 2: If any type of of the offered numbers (12, 15, 18) is a multiple of 2, divide it by 2 and write the quotient listed below it. Lug down any number that is no divisible through the element number.Step 3: continue the actions until just 1s space left in the critical row.

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

### LCM the 12, 15, and 18 by element Factorization

Prime administrate of 12, 15, and also 18 is (2 × 2 × 3) = 22 × 31, (3 × 5) = 31 × 51, and also (2 × 3 × 3) = 21 × 32 respectively. LCM of 12, 15, and also 18 have the right to be acquired by multiplying prime factors raised to your respective highest possible power, i.e. 22 × 32 × 51 = 180.Hence, the LCM that 12, 15, and 18 by element factorization is 180.

### LCM the 12, 15, and 18 by Listing Multiples

To calculate the LCM the 12, 15, 18 by listing the end the usual multiples, we deserve to follow the given listed below steps:

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

∴ The least common multiple of 12, 15, and 18 = 180.

☛ likewise Check:

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

Solution:

The relation between GCD and also LCM the 12, 15, and also 18 is given 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 that (12, 15), (15, 18), (12, 18) and also (12, 15, 18) = 3, 3, 6 and 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.

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

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

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

### How to discover the LCM the 12, 15, and 18 by element Factorization?

To find the LCM the 12, 15, and 18 utilizing prime factorization, us will uncover the prime factors, (12 = 22 × 31), (15 = 31 × 51), and also (18 = 21 × 32). LCM that 12, 15, and also 18 is the product the prime determinants raised to their respective highest exponent among the number 12, 15, and 18.⇒ LCM of 12, 15, 18 = 22 × 32 × 51 = 180.

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### What space the techniques to uncover LCM the 12, 15, 18?

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