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LCM of 3 and 3

LCM of 3 and 3 is the smallest number among all multiples of 3. The first few multiples of 3 are (3, 6, 9, 12, 15, 18, 21, . . . ). There are 2 commonly used methods to find LCM of 3 and 3 - by listing multiples, and by division method.

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

What is the LCM of 3 and 3?

Answer: LCM of 3 and 3 is 3.

Explanation:

The LCM of non-zero integers, x(3) and y(3), is the smallest positive integer m(3) that is divisible by both x(3) and y(3) without any remainder.

Methods to Find LCM of 3 and 3

Let's look at the different methods for finding the LCM of 3 and 3.

By Division Method
By Listing Multiples

LCM of 3 and 3 by Division Method

To calculate the LCM of 3 and 3 by the division method, we will divide the numbers(3, 3) 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 3 and 3.

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

The LCM of 3 and 3 by division method is given as, LCM(3, 3) = 3.

LCM of 3 and 3 by Listing Multiples

To calculate the LCM of 3 and 3 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ).
Step 2: The smallest common multiple of 3 and 3 is 3.

∴ The least common multiple of 3 and 3 = 3.

☛ Also Check:

LCM of 3 and 3 Examples

Example 1: Verify the relationship between GCF and LCM of 3 and 3.

Solution:

The relation between GCF and LCM of 3 and 3 is given as,
LCM(3, 3) × GCF(3, 3) = Product of 3, 3
LCM(3, 3) = 3
GCF(3, 3) = 3
LHS = LCM(3, 3) × GCF(3, 3) = 3 × 3 = 9
RHS = Product of 3, 3 = 3 × 3 = 9
⇒ LHS = RHS = 9
Hence, verified.
Example 2: The product of two numbers is 9. If their GCD is 3, what is their LCM?

Solution:

Given: GCD = 3
product of numbers = 9
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 9/3
Therefore, the LCM is 3.
The probable combination for the given case is LCM(3, 3) = 3.
Example 2: The GCD and LCM of two numbers are 3 and 3 respectively. If one number is 3, find the other number.

Solution:

Let the other number be x.
∵ GCD × LCM = 3 × x
⇒ x = (GCD × LCM)/3
⇒ x = (3 × 3)/3
⇒ x = 3
Therefore, the other number is 3.

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FAQs on LCM of 3 and 3

What is the LCM of 3 and 3?

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

What are the Methods to Find LCM of 3 and 3?

The commonly used methods to find the LCM of 3 and 3 are:

Listing Multiples
Division Method

What is the Least Perfect Square Divisible by 3 and 3?

The least number divisible by 3 and 3 = LCM(3, 3)
LCM of 3 and 3 = 3.
⇒ Least perfect square divisible by each 3 and 3 = 3 × 3 = 9 [Square root of 9 = √9 = ±3]
Therefore, 9 is the required number.

If the LCM of 3 and 3 is 3, Find its GCF.

LCM(3, 3) × GCF(3, 3) = 3 × 3
Since the LCM of 3 and 3 = 3
⇒ 3 × GCF(3, 3) = 9
Therefore, the greatest common factor = 9/3 = 3.

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

The following equation can be used to express the relation between GCF and LCM of 3 and 3, i.e. GCF × LCM = 3 × 3.

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