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LCM of 4 and 4

LCM of 4 and 4 is the smallest number among all multiples of 4. The first few multiples of 4 are (4, 8, 12, 16, 20, 24, . . . ). There are 2 commonly used methods to find LCM of 4 and 4 - by division method, and by listing multiples.

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

What is the LCM of 4 and 4?

Answer: LCM of 4 and 4 is 4.

Explanation:

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

Methods to Find LCM of 4 and 4

The methods to find the LCM of 4 and 4 are explained below.

By Division Method
By Listing Multiples

LCM of 4 and 4 by Division Method

To calculate the LCM of 4 and 4 by the division method, we will divide the numbers(4, 4) by their prime factors, as long as at least one of the numbers is evenly divisible by a prime number. The product of these divisors gives the LCM of 4 and 4.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 4. Write this prime number(2) on the left of the given numbers(4 and 4), separated as per the ladder arrangement.
Step 2: Divide the given numbers (4, 4) by 2 and write the quotient below them.
Step 3: Continue the steps until only 1s are left in the last row.

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

LCM of 4 and 4 by Listing Multiples

To calculate the LCM of 4 and 4 by listing out the multiples, we can follow the given below steps:

Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, . . . ).
Step 2: The smallest common multiple of 4 and 4 is 4.

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

☛ Also Check:

LCM of 4 and 4 Examples

Example 1: The GCD and LCM of two numbers are 4 and 4 respectively. If one number is 4, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 4 × z
⇒ z = (GCD × LCM)/4
⇒ z = (4 × 4)/4
⇒ z = 4
Therefore, the other number is 4.
Example 2: The product of two numbers is 16. If their GCD is 4, what is their LCM?

Solution:

Given: GCD = 4
product of numbers = 16
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 16/4
Therefore, the LCM is 4.
The probable combination for the given case is LCM(4, 4) = 4.
Example 3: Verify the relationship between GCF and LCM of 4 and 4.

Solution:

The relation between GCF and LCM of 4 and 4 is given as,
LCM(4, 4) × GCF(4, 4) = Product of 4, 4
LCM(4, 4) = 4
GCF(4, 4) = 4
LHS = LCM(4, 4) × GCF(4, 4) = 4 × 4 = 16
RHS = Product of 4, 4 = 4 × 4 = 16
⇒ LHS = RHS = 16
Hence, verified.

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FAQs on LCM of 4 and 4

What is the LCM of 4 and 4?

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

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

LCM(4, 4) × GCF(4, 4) = 4 × 4
Since the LCM of 4 and 4 = 4
⇒ 4 × GCF(4, 4) = 16
Therefore, the greatest common factor = 16/4 = 4.

What are the Methods to Find LCM of 4 and 4?

The commonly used methods to find the LCM of 4 and 4 are:

Division Method
Listing Multiples

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

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

Which of the following is the LCM of 4 and 4? 20, 4, 40, 45

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

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