LCM that 8, 12, and 16 is the smallest number among all typical multiples that 8, 12, and also 16. The first few multiples the 8, 12, and also 16 room (8, 16, 24, 32, 40 . . .), (12, 24, 36, 48, 60 . . .), and (16, 32, 48, 64, 80 . . .) respectively. There room 3 commonly used methods to find LCM the 8, 12, 16 - through listing multiples, by department method, and by element factorization.

You are watching: Lcm of 8, 12,16

1.LCM the 8, 12, and 16
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM the 8, 12, and also 16 is 48.

*

Explanation:

The LCM of 3 non-zero integers, a(8), b(12), and also c(16), is the smallest optimistic integer m(48) the is divisible by a(8), b(12), and also c(16) without any remainder.


The techniques to find the LCM the 8, 12, and also 16 are defined below.

By division MethodBy Listing MultiplesBy element Factorization Method

LCM of 8, 12, and 16 by department Method

*

To calculation the LCM of 8, 12, and 16 through the department method, we will certainly divide the numbers(8, 12, 16) by your prime determinants (preferably common). The product of this divisors offers the LCM the 8, 12, and 16.

Step 2: If any kind of of the provided numbers (8, 12, 16) is a lot of of 2, divide it by 2 and write the quotient listed below it. Carry down any type of number the is no divisible by the element number.Step 3: proceed the actions until only 1s space left in the critical row.

The LCM of 8, 12, and 16 is the product of every prime numbers on the left, i.e. LCM(8, 12, 16) by division method = 2 × 2 × 2 × 2 × 3 = 48.

LCM of 8, 12, and 16 by Listing Multiples

*

To calculate the LCM of 8, 12, 16 through listing out the typical multiples, we can follow the given below steps:

Step 1: list a couple of multiples the 8 (8, 16, 24, 32, 40 . . .), 12 (12, 24, 36, 48, 60 . . .), and 16 (16, 32, 48, 64, 80 . . .).Step 2: The common multiples indigenous the multiples of 8, 12, and also 16 space 48, 96, . . .Step 3: The smallest usual multiple that 8, 12, and 16 is 48.

∴ The least typical multiple the 8, 12, and also 16 = 48.

LCM the 8, 12, and 16 by prime Factorization

Prime administrate of 8, 12, and 16 is (2 × 2 × 2) = 23, (2 × 2 × 3) = 22 × 31, and (2 × 2 × 2 × 2) = 24 respectively. LCM that 8, 12, and 16 deserve to be obtained by multiply prime factors raised to your respective greatest power, i.e. 24 × 31 = 48.Hence, the LCM that 8, 12, and also 16 by prime factorization is 48.

☛ likewise Check:


Example 2: Verify the relationship between the GCD and also LCM the 8, 12, and also 16.

Solution:

The relation in between GCD and LCM the 8, 12, and 16 is offered as,LCM(8, 12, 16) = <(8 × 12 × 16) × GCD(8, 12, 16)>/⇒ element factorization of 8, 12 and 16:

8 = 2312 = 22 × 3116 = 24

∴ GCD of (8, 12), (12, 16), (8, 16) and (8, 12, 16) = 4, 4, 8 and 4 respectively.Now, LHS = LCM(8, 12, 16) = 48.And, RHS = <(8 × 12 × 16) × GCD(8, 12, 16)>/ = <(1536) × 4>/<4 × 4 × 8> = 48LHS = RHS = 48.Hence verified.


Example 3: find the the smallest number that is divisible by 8, 12, 16 exactly.

Solution:

The the smallest number the is divisible by 8, 12, and also 16 precisely is their LCM.⇒ Multiples of 8, 12, and also 16:

Multiples the 8 = 8, 16, 24, 32, 40, 48, 56, . . . .Multiples that 12 = 12, 24, 36, 48, 60, 72, 84, . . . .Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, . . . .

Therefore, the LCM the 8, 12, and 16 is 48.


Show systems >

go come slidego to slidego to slide


*


FAQs on LCM of 8, 12, and 16

What is the LCM that 8, 12, and 16?

The LCM of 8, 12, and 16 is 48. To uncover the least typical multiple (LCM) of 8, 12, and 16, we require to discover the multiples of 8, 12, and 16 (multiples that 8 = 8, 16, 24, 32, 48 . . . .; multiples of 12 = 12, 24, 36, 48 . . . .; multiples of 16 = 16, 32, 48, 64 . . . .) and choose the smallest multiple that is precisely divisible by 8, 12, and 16, i.e., 48.

Which that the following is the LCM that 8, 12, and 16? 11, 81, 48, 36

The value of LCM the 8, 12, 16 is the smallest usual multiple of 8, 12, and also 16. The number to solve the given condition is 48.

What is the Relation in between GCF and also LCM that 8, 12, 16?

The adhering to equation can be offered to to express the relation in between GCF and also LCM of 8, 12, 16, i.e. LCM(8, 12, 16) = <(8 × 12 × 16) × GCF(8, 12, 16)>/.

See more: How Much Is 0.5 Ml In Tsp - Ml To Teaspoons (Tsp) Converter

How to discover the LCM of 8, 12, and 16 by element Factorization?

To uncover the LCM of 8, 12, and 16 making use of prime factorization, we will find the prime factors, (8 = 23), (12 = 22 × 31), and also (16 = 24). LCM of 8, 12, and also 16 is the product of prime components raised to your respective highest exponent among the numbers 8, 12, and 16.⇒ LCM the 8, 12, 16 = 24 × 31 = 48.