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 4 are (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), and (4, 8, 12, 16, 20 . . .) respectively. There are 3 commonly used methods to find LCM of 2, 3, 4 - by listing multiples, by prime factorization, and by division method.

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

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

The LCM of three non-zero integers, a(2), b(3), and 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 find the LCM of 2, 3, and 4 are explained below.

By Prime Factorization MethodBy Listing MultiplesBy Division Method

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

Prime factorization of 2, 3, and 4 is (2) = 21, (3) = 31, and (2 × 2) = 22 respectively. LCM of 2, 3, and 4 can be obtained by multiplying prime factors raised to their respective 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 4 by Listing Multiples To calculate the LCM of 2, 3, 4 by listing out the common multiples, we can follow the given below steps:

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

∴ The least common 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 division method, 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 of the given numbers (2, 3, 4) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.Step 3: Continue the steps until only 1s are left in the last row.

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

☛ Also Check:

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

Solution:

The relation between GCD and LCM of 2, 3, and 4 is given 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 verified.

Example 2: Calculate the LCM of 2, 3, and 4 using the GCD of the given 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 smallest number that is divisible by 2, 3, 4 exactly.

Solution:

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

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

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

The LCM of 2, 3, and 4 is 12. To find the LCM (least common multiple) of 2, 3, and 4, we need to find the multiples of 2, 3, and 4 (multiples of 2 = 2, 4, 6, 8, 12 . . . .; multiples of 3 = 3, 6, 9, 12 . . . .; multiples of 4 = 4, 8, 12, 16 . . . .) and choose the smallest multiple that is exactly divisible by 2, 3, and 4, i.e., 12.

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

The commonly used methods to find the LCM of 2, 3, 4 are:

Prime Factorization MethodDivision MethodListing Multiples

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

The following equation can be used 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)>/.

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

The value of LCM of 2, 3, 4 is the smallest common multiple of 2, 3, and 4. The number satisfying the given condition is 12.