LCM of 2, 3, and 4 is the smallest number among all common multiples of 2, 3, and 4. The first few multiples of 2, 3, and also 4 are (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), and (4, 8, 12, 16, 20 . . .) respectively. Tbelow are 3 commonly offered approaches to discover LCM of 2, 3, 4 - by listing multiples, by prime factorization, and also by division technique.

You are watching: Least common multiple of 2 3 4

1.LCM of 2, 3, and 4
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 2, 3, and also 4 is 12.

*

Explanation:

The LCM of three non-zero integers, a(2), b(3), and also c(4), is the smallest positive integer m(12) that is divisible by a(2), b(3), and c(4) without any remainder.


The methods to discover the LCM of 2, 3, and also 4 are defined below.

By Prime Factorization MethodBy Listing MultiplesBy Division Method

LCM of 2, 3, and also 4 by Prime Factorization

Prime factorization of 2, 3, and 4 is (2) = 21, (3) = 31, and also (2 × 2) = 22 respectively. LCM of 2, 3, and 4 can be obtained by multiplying prime determinants raised to their corresponding highest power, i.e. 22 × 31 = 12.Hence, the LCM of 2, 3, and 4 by prime factorization is 12.

LCM of 2, 3, and also 4 by Listing Multiples

*

To calculate the LCM of 2, 3, 4 by listing out the prevalent multiples, we can follow the given listed below steps:

Step 1: List a few multiples of 2 (2, 4, 6, 8, 10 . . .), 3 (3, 6, 9, 12, 15 . . .), and also 4 (4, 8, 12, 16, 20 . . .).Step 2: The prevalent multiples from the multiples of 2, 3, and also 4 are 12, 24, . . .Step 3: The smallest common multiple of 2, 3, and also 4 is 12.

∴ The leastern prevalent multiple of 2, 3, and 4 = 12.

LCM of 2, 3, and 4 by Division Method

*

To calculate the LCM of 2, 3, and 4 by the department approach, we will divide the numbers(2, 3, 4) by their prime factors (preferably common). The product of these divisors gives the LCM of 2, 3, and 4.

Step 2: If any type of of the given numbers (2, 3, 4) is a multiple of 2, divide it by 2 and also create the quotient below it. Bring down any number that is not divisible by the prime number.Tip 3: Continue the measures until only 1s are left in the last row.

The LCM of 2, 3, and also 4 is the product of all prime numbers on the left, i.e. LCM(2, 3, 4) by division technique = 2 × 2 × 3 = 12.

☛ Also Check:


Example 1: Verify the partnership between the GCD and also LCM of 2, 3, and 4.

Solution:

The relation in between GCD and LCM of 2, 3, and 4 is offered as,LCM(2, 3, 4) = <(2 × 3 × 4) × GCD(2, 3, 4)>/⇒ Prime factorization of 2, 3 and 4:

2 = 213 = 314 = 22

∴ GCD of (2, 3), (3, 4), (2, 4) and (2, 3, 4) = 1, 1, 2 and 1 respectively.Now, LHS = LCM(2, 3, 4) = 12.And, RHS = <(2 × 3 × 4) × GCD(2, 3, 4)>/ = <(24) × 1>/<1 × 1 × 2> = 12LHS = RHS = 12.Hence showed.


Example 2: Calculate the LCM of 2, 3, and 4 using the GCD of the provided numbers.

Solution:

Prime factorization of 2, 3, 4:

2 = 213 = 314 = 22

As such, GCD(2, 3) = 1, GCD(3, 4) = 1, GCD(2, 4) = 2, GCD(2, 3, 4) = 1We understand,LCM(2, 3, 4) = <(2 × 3 × 4) × GCD(2, 3, 4)>/LCM(2, 3, 4) = (24 × 1)/(1 × 1 × 2) = 12⇒LCM(2, 3, 4) = 12


Example 3: Find the smallest number that is divisible by 2, 3, 4 precisely.

Solution:

The smallest number that is divisible by 2, 3, and also 4 exactly is their LCM.⇒ Multiples of 2, 3, and also 4:

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, . . . .Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, . . . .Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, . . . .

As such, the LCM of 2, 3, and 4 is 12.


Show Equipment >

go to slidego to slidego to slide


*


FAQs on LCM of 2, 3, and 4

What is the LCM of 2, 3, and also 4?

The LCM of 2, 3, and 4 is 12. To uncover the LCM (leastern widespread multiple) of 2, 3, and 4, we should discover the multiples of 2, 3, and also 4 (multiples of 2 = 2, 4, 6, 8, 12 . . . .; multiples of 3 = 3, 6, 9, 12 . . . .; multiples of 4 = 4, 8, 12, 16 . . . .) and also choose the smallest multiple that is specifically divisible by 2, 3, and 4, i.e., 12.

What are the Methods to Find LCM of 2, 3, 4?

The typically offered techniques to discover the LCM of 2, 3, 4 are:

Prime Factorization MethodDivision MethodListing Multiples

What is the Relation Between GCF and also LCM of 2, 3, 4?

The following equation deserve to be provided to express the relation between GCF and LCM of 2, 3, 4, i.e. LCM(2, 3, 4) = <(2 × 3 × 4) × GCF(2, 3, 4)>/.

See more: Who Won Baja Or Pitch Black For The Win!, Pitch Black

Which of the following is the LCM of 2, 3, and 4? 120, 12, 45, 21

The worth of LCM of 2, 3, 4 is the smallest common multiple of 2, 3, and also 4. The number satisfying the offered problem is 12.