LCM the 8, 12, and 15 is the the smallest number amongst all usual multiples of 8, 12, and also 15. The first couple of multiples that 8, 12, and 15 are (8, 16, 24, 32, 40 . . .), (12, 24, 36, 48, 60 . . .), and also (15, 30, 45, 60, 75 . . .) respectively. There space 3 typically used approaches to find LCM the 8, 12, 15 - by prime factorization, by division method, and also by listing multiples.

You are watching: What is the least common multiple of 8 and 12?

1.LCM the 8, 12, and 15
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM the 8, 12, and also 15 is 120.

*

Explanation:

The LCM of 3 non-zero integers, a(8), b(12), and also c(15), is the smallest hopeful integer m(120) the is divisible by a(8), b(12), and c(15) without any kind of remainder.


The techniques to uncover the LCM of 8, 12, and 15 are defined below.

By prime Factorization MethodBy department MethodBy Listing Multiples

LCM that 8, 12, and 15 by element Factorization

Prime administrate of 8, 12, and also 15 is (2 × 2 × 2) = 23, (2 × 2 × 3) = 22 × 31, and (3 × 5) = 31 × 51 respectively. LCM of 8, 12, and 15 deserve to be acquired by multiply prime factors raised to your respective highest power, i.e. 23 × 31 × 51 = 120.Hence, the LCM of 8, 12, and also 15 by prime factorization is 120.

LCM that 8, 12, and 15 by department Method

*

To calculate the LCM that 8, 12, and also 15 through the department method, we will divide the numbers(8, 12, 15) by their prime components (preferably common). The product of this divisors provides the LCM the 8, 12, and 15.

Step 2: If any of the offered numbers (8, 12, 15) is a multiple of 2, divide it through 2 and write the quotient listed below it. Bring down any kind of number the is not divisible by the element number.Step 3: proceed the measures until just 1s are left in the critical row.

The LCM of 8, 12, and also 15 is the product of all prime numbers on the left, i.e. LCM(8, 12, 15) by division method = 2 × 2 × 2 × 3 × 5 = 120.

LCM the 8, 12, and 15 by Listing Multiples

*

To calculate the LCM of 8, 12, 15 by listing out the common multiples, we can follow the given listed below steps:

Step 1: list a few multiples of 8 (8, 16, 24, 32, 40 . . .), 12 (12, 24, 36, 48, 60 . . .), and 15 (15, 30, 45, 60, 75 . . .).Step 2: The common multiples native the multiples of 8, 12, and also 15 space 120, 240, . . .Step 3: The smallest usual multiple the 8, 12, and also 15 is 120.

∴ The least usual multiple that 8, 12, and 15 = 120.

☛ additionally Check:


Example 1: Verify the relationship in between the GCD and also LCM the 8, 12, and also 15.

Solution:

The relation in between GCD and LCM the 8, 12, and also 15 is provided as,LCM(8, 12, 15) = <(8 × 12 × 15) × GCD(8, 12, 15)>/⇒ element factorization of 8, 12 and also 15:

8 = 2312 = 22 × 3115 = 31 × 51

∴ GCD that (8, 12), (12, 15), (8, 15) and (8, 12, 15) = 4, 3, 1 and 1 respectively.Now, LHS = LCM(8, 12, 15) = 120.And, RHS = <(8 × 12 × 15) × GCD(8, 12, 15)>/ = <(1440) × 1>/<4 × 3 × 1> = 120LHS = RHS = 120.Hence verified.


Example 2: calculate the LCM the 8, 12, and 15 utilizing the GCD that the given numbers.

Solution:

Prime administer of 8, 12, 15:

8 = 2312 = 22 × 3115 = 31 × 51

Therefore, GCD(8, 12) = 4, GCD(12, 15) = 3, GCD(8, 15) = 1, GCD(8, 12, 15) = 1We know,LCM(8, 12, 15) = <(8 × 12 × 15) × GCD(8, 12, 15)>/LCM(8, 12, 15) = (1440 × 1)/(4 × 3 × 1) = 120⇒LCM(8, 12, 15) = 120


Example 3: discover the the smallest number the is divisible by 8, 12, 15 exactly.

Solution:

The smallest number the is divisible by 8, 12, and 15 exactly is their LCM.⇒ Multiples that 8, 12, and also 15:

Multiples the 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, . . . .Multiples that 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . .Multiples that 15 = 15, 30, 45, 60, 75, 90, 105, 120, . . . .

Therefore, the LCM of 8, 12, and 15 is 120.


Show equipment >

go to slidego come slidego to slide


*


FAQs on LCM that 8, 12, and 15

What is the LCM that 8, 12, and 15?

The LCM of 8, 12, and also 15 is 120. To find the LCM (least typical multiple) of 8, 12, and also 15, we need to find the multiples of 8, 12, and 15 (multiples the 8 = 8, 16, 24, 32 . . . . 120 . . . . ; multiples of 12 = 12, 24, 36, 48 . . . . 120 . . . . ; multiples that 15 = 15, 30, 45, 60 . . . . 120 . . . . ) and also choose the the smallest multiple the is specifically divisible by 8, 12, and 15, i.e., 120.

What space the techniques to uncover LCM the 8, 12, 15?

The commonly used approaches to discover the LCM of 8, 12, 15 are:

Prime factorization MethodListing MultiplesDivision Method

How to find the LCM the 8, 12, and 15 by prime Factorization?

To find the LCM of 8, 12, and also 15 using prime factorization, us will find the prime factors, (8 = 23), (12 = 22 × 31), and (15 = 31 × 51). LCM of 8, 12, and also 15 is the product that prime factors raised to your respective greatest exponent among the number 8, 12, and 15.⇒ LCM that 8, 12, 15 = 23 × 31 × 51 = 120.

See more: Why Do Bridge Ices Before Road Sign Meaning, Why Do Bridges Ice Over Before Roads

What is the the very least Perfect Square Divisible by 8, 12, and 15?

The least number divisible through 8, 12, and 15 = LCM(8, 12, 15)LCM of 8, 12, and 15 = 2 × 2 × 2 × 3 × 5 ⇒ the very least perfect square divisible by every 8, 12, and 15 = LCM(8, 12, 15) × 2 × 3 × 5 = 3600 Therefore, 3600 is the compelled number.