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LCM of 2 and 4

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

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

What is the LCM of 2 and 4?

Answer: LCM of 2 and 4 is 4.

Explanation:

The LCM of two non-zero integers, x(2) and y(4), is the smallest positive integer m(4) that is divisible by both x(2) and y(4) without any remainder.

Methods to Find LCM of 2 and 4

Let's look at the different methods for finding the LCM of 2 and 4.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 2 and 4 by Prime Factorization

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

LCM of 2 and 4 by Listing Multiples

To calculate the LCM of 2 and 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, . . . ) and 4 (4, 8, 12, 16, . . . . )
Step 2: The common multiples from the multiples of 2 and 4 are 4, 8, . . .
Step 3: The smallest common multiple of 2 and 4 is 4.

∴ The least common multiple of 2 and 4 = 4.

LCM of 2 and 4 by Division Method

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

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 4. Write this prime number(2) on the left of the given numbers(2 and 4), separated as per the ladder arrangement.
Step 2: If any of the given numbers (2, 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 and 4 is the product of all prime numbers on the left, i.e. LCM(2, 4) by division method = 2 × 2 = 4.

☛ Also Check:

LCM of 2 and 4 Examples

Example 1: The product of two numbers is 8. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2
product of numbers = 8
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 8/2
Therefore, the LCM is 4.
The probable combination for the given case is LCM(2, 4) = 4.
Example 2: The GCD and LCM of two numbers are 2 and 4 respectively. If one number is 2, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 2 × m
⇒ m = (GCD × LCM)/2
⇒ m = (2 × 4)/2
⇒ m = 4
Therefore, the other number is 4.
Example 3: Find the smallest number that is divisible by 2 and 4 exactly.

Solution:

The smallest number that is divisible by 2 and 4 exactly is their LCM.
⇒ Multiples of 2 and 4:
- Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, . . . .
- Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, . . . .
Therefore, the LCM of 2 and 4 is 4.

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FAQs on LCM of 2 and 4

What is the LCM of 2 and 4?

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

How to Find the LCM of 2 and 4 by Prime Factorization?

To find the LCM of 2 and 4 using prime factorization, we will find the prime factors, (2 = 2) and (4 = 2 × 2). LCM of 2 and 4 is the product of prime factors raised to their respective highest exponent among the numbers 2 and 4.
⇒ LCM of 2, 4 = 2² = 4.

If the LCM of 4 and 2 is 4, Find its GCF.

LCM(4, 2) × GCF(4, 2) = 4 × 2
Since the LCM of 4 and 2 = 4
⇒ 4 × GCF(4, 2) = 8
Therefore, the GCF (greatest common factor) = 8/4 = 2.

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

The following equation can be used to express the relation between GCF and LCM of 2 and 4, i.e. GCF × LCM = 2 × 4.

Which of the following is the LCM of 2 and 4? 5, 4, 30, 32

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

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