LCM of 2, 3, and also 4 is the smallest number among all typical multiples of 2, 3, and 4. The first few multiples the 2, 3, and 4 are (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), and (4, 8, 12, 16, 20 . . .) respectively. There are 3 commonly used techniques to find LCM the 2, 3, 4 - by listing multiples, by prime factorization, and also by division method.

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1.LCM that 2, 3, and also 4
2.List the Methods
3.Solved Examples
4.FAQs

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

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Explanation:

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


The techniques to discover the LCM the 2, 3, and also 4 are described below.

By prime Factorization MethodBy Listing MultiplesBy department Method

LCM that 2, 3, and also 4 by element Factorization

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

LCM of 2, 3, and 4 through Listing Multiples

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

Step 1: list a couple of multiples that 2 (2, 4, 6, 8, 10 . . .), 3 (3, 6, 9, 12, 15 . . .), and also 4 (4, 8, 12, 16, 20 . . .).Step 2: The usual multiples from the multiples that 2, 3, and 4 space 12, 24, . . .Step 3: The smallest common multiple of 2, 3, and 4 is 12.

∴ The least usual multiple that 2, 3, and also 4 = 12.

LCM the 2, 3, and 4 by division Method

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To calculate the LCM of 2, 3, and also 4 by the division method, we will divide the numbers(2, 3, 4) by your prime components (preferably common). The product of this divisors offers the LCM the 2, 3, and also 4.

Step 2: If any type of of the given numbers (2, 3, 4) is a lot of of 2, divide it by 2 and also write the quotient listed below it. Bring down any number that is not divisible through the prime number.Step 3: proceed the procedures until only 1s are left in the last row.

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

☛ likewise Check:


Example 1: Verify the relationship in between the GCD and also LCM that 2, 3, and also 4.

Solution:

The relation in between GCD and LCM the 2, 3, and also 4 is provided as,LCM(2, 3, 4) = <(2 × 3 × 4) × GCD(2, 3, 4)>/⇒ prime factorization that 2, 3 and 4:

2 = 213 = 314 = 22

∴ GCD that (2, 3), (3, 4), (2, 4) and also (2, 3, 4) = 1, 1, 2 and also 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 verified.


Example 2: calculation the LCM of 2, 3, and 4 making use of the GCD that the offered numbers.

Solution:

Prime factorization of 2, 3, 4:

2 = 213 = 314 = 22

Therefore, GCD(2, 3) = 1, GCD(3, 4) = 1, GCD(2, 4) = 2, GCD(2, 3, 4) = 1We know,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 the smallest number that is divisible by 2, 3, 4 exactly.

Solution:

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

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

Therefore, the LCM of 2, 3, and 4 is 12.


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FAQs on LCM the 2, 3, and also 4

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

The LCM that 2, 3, and also 4 is 12. To find the LCM (least typical multiple) of 2, 3, and also 4, we need to 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 that 4 = 4, 8, 12, 16 . . . .) and also choose the the smallest multiple the is precisely divisible through 2, 3, and 4, i.e., 12.

What room the techniques to find LCM that 2, 3, 4?

The frequently used methods to uncover the LCM that 2, 3, 4 are:

Prime factorization MethodDivision MethodListing Multiples

What is the Relation in between GCF and also LCM the 2, 3, 4?

The complying with equation can be offered to refer the relation in between GCF and also LCM that 2, 3, 4, i.e. LCM(2, 3, 4) = <(2 × 3 × 4) × GCF(2, 3, 4)>/.

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Which that the complying with is the LCM that 2, 3, and also 4? 120, 12, 45, 21

The worth of LCM of 2, 3, 4 is the smallest typical multiple the 2, 3, and 4. The number satisfying the given problem is 12.