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LCM of 3 and 9

LCM of 3 and 9 is the smallest number among all common multiples of 3 and 9. The first few multiples of 3 and 9 are (3, 6, 9, 12, 15, . . . ) and (9, 18, 27, 36, 45, 54, 63, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 9 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 3 and 9
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 3 and 9?

Answer: LCM of 3 and 9 is 9.

Explanation:

The LCM of two non-zero integers, x(3) and y(9), is the smallest positive integer m(9) that is divisible by both x(3) and y(9) without any remainder.

Methods to Find LCM of 3 and 9

Let's look at the different methods for finding the LCM of 3 and 9.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 3 and 9 by Division Method

To calculate the LCM of 3 and 9 by the division method, we will divide the numbers(3, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 9.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 9. Write this prime number(3) on the left of the given numbers(3 and 9), separated as per the ladder arrangement.
Step 2: If any of the given numbers (3, 9) is a multiple of 3, divide it by 3 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 3 and 9 is the product of all prime numbers on the left, i.e. LCM(3, 9) by division method = 3 × 3 = 9.

LCM of 3 and 9 by Prime Factorization

Prime factorization of 3 and 9 is (3) = 3¹ and (3 × 3) = 3² respectively. LCM of 3 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² = 9.
Hence, the LCM of 3 and 9 by prime factorization is 9.

LCM of 3 and 9 by Listing Multiples

To calculate the LCM of 3 and 9 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, . . . ) and 9 (9, 18, 27, 36, 45, 54, 63, . . . . )
Step 2: The common multiples from the multiples of 3 and 9 are 9, 18, . . .
Step 3: The smallest common multiple of 3 and 9 is 9.

∴ The least common multiple of 3 and 9 = 9.

☛ Also Check:

LCM of 3 and 9 Examples

Example 1: The GCD and LCM of two numbers are 3 and 9 respectively. If one number is 9, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 9 × m
⇒ m = (GCD × LCM)/9
⇒ m = (3 × 9)/9
⇒ m = 3
Therefore, the other number is 3.
Example 2: Find the smallest number that is divisible by 3 and 9 exactly.

Solution:

The smallest number that is divisible by 3 and 9 exactly is their LCM.
⇒ Multiples of 3 and 9:
- Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, . . . .
- Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, . . . .
Therefore, the LCM of 3 and 9 is 9.
Example 3: The product of two numbers is 27. If their GCD is 3, what is their LCM?

Solution:

Given: GCD = 3
product of numbers = 27
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 27/3
Therefore, the LCM is 9.
The probable combination for the given case is LCM(3, 9) = 9.

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FAQs on LCM of 3 and 9

What is the LCM of 3 and 9?

The LCM of 3 and 9 is 9. To find the least common multiple (LCM) of 3 and 9, we need to find the multiples of 3 and 9 (multiples of 3 = 3, 6, 9, 12; multiples of 9 = 9, 18, 27, 36) and choose the smallest multiple that is exactly divisible by 3 and 9, i.e., 9.

What are the Methods to Find LCM of 3 and 9?

The commonly used methods to find the LCM of 3 and 9 are:

Division Method
Prime Factorization Method
Listing Multiples

What is the Least Perfect Square Divisible by 3 and 9?

The least number divisible by 3 and 9 = LCM(3, 9)
LCM of 3 and 9 = 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 3 and 9 = 9 [Square root of 9 = √9 = ±3]
Therefore, 9 is the required number.

Which of the following is the LCM of 3 and 9? 15, 9, 2, 42

The value of LCM of 3, 9 is the smallest common multiple of 3 and 9. The number satisfying the given condition is 9.

If the LCM of 9 and 3 is 9, Find its GCF.

LCM(9, 3) × GCF(9, 3) = 9 × 3
Since the LCM of 9 and 3 = 9
⇒ 9 × GCF(9, 3) = 27
Therefore, the GCF (greatest common factor) = 27/9 = 3.

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