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LCM of 9 and 18

LCM of 9 and 18 is the smallest number among all common multiples of 9 and 18. The first few multiples of 9 and 18 are (9, 18, 27, 36, . . . ) and (18, 36, 54, 72, 90, 108, 126, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 18 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 9 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 9 and 18?

Answer: LCM of 9 and 18 is 18.

Explanation:

The LCM of two non-zero integers, x(9) and y(18), is the smallest positive integer m(18) that is divisible by both x(9) and y(18) without any remainder.

Methods to Find LCM of 9 and 18

Let's look at the different methods for finding the LCM of 9 and 18.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 9 and 18 by Prime Factorization

Prime factorization of 9 and 18 is (3 × 3) = 3² and (2 × 3 × 3) = 2¹ × 3² respectively. LCM of 9 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² = 18.
Hence, the LCM of 9 and 18 by prime factorization is 18.

LCM of 9 and 18 by Listing Multiples

To calculate the LCM of 9 and 18 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 9 (9, 18, 27, 36, . . . ) and 18 (18, 36, 54, 72, 90, 108, 126, . . . . )
Step 2: The common multiples from the multiples of 9 and 18 are 18, 36, . . .
Step 3: The smallest common multiple of 9 and 18 is 18.

∴ The least common multiple of 9 and 18 = 18.

LCM of 9 and 18 by Division Method

To calculate the LCM of 9 and 18 by the division method, we will divide the numbers(9, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 18.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 18. Write this prime number(2) on the left of the given numbers(9 and 18), separated as per the ladder arrangement.
Step 2: If any of the given numbers (9, 18) 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 9 and 18 is the product of all prime numbers on the left, i.e. LCM(9, 18) by division method = 2 × 3 × 3 = 18.

☛ Also Check:

LCM of 9 and 18 Examples

Example 1: Verify the relationship between GCF and LCM of 9 and 18.

Solution:

The relation between GCF and LCM of 9 and 18 is given as,
LCM(9, 18) × GCF(9, 18) = Product of 9, 18
Prime factorization of 9 and 18 is given as, 9 = (3 × 3) = 3² and 18 = (2 × 3 × 3) = 2¹ × 3²
LCM(9, 18) = 18
GCF(9, 18) = 9
LHS = LCM(9, 18) × GCF(9, 18) = 18 × 9 = 162
RHS = Product of 9, 18 = 9 × 18 = 162
⇒ LHS = RHS = 162
Hence, verified.
Example 2: The product of two numbers is 162. If their GCD is 9, what is their LCM?

Solution:

Given: GCD = 9
product of numbers = 162
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 162/9
Therefore, the LCM is 18.
The probable combination for the given case is LCM(9, 18) = 18.
Example 3: The GCD and LCM of two numbers are 9 and 18 respectively. If one number is 18, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 18 × b
⇒ b = (GCD × LCM)/18
⇒ b = (9 × 18)/18
⇒ b = 9
Therefore, the other number is 9.

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FAQs on LCM of 9 and 18

What is the LCM of 9 and 18?

The LCM of 9 and 18 is 18. To find the LCM of 9 and 18, we need to find the multiples of 9 and 18 (multiples of 9 = 9, 18, 27, 36; multiples of 18 = 18, 36, 54, 72) and choose the smallest multiple that is exactly divisible by 9 and 18, i.e., 18.

How to Find the LCM of 9 and 18 by Prime Factorization?

To find the LCM of 9 and 18 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (18 = 2 × 3 × 3). LCM of 9 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 18.
⇒ LCM of 9, 18 = 2¹ × 3² = 18.

If the LCM of 18 and 9 is 18, Find its GCF.

LCM(18, 9) × GCF(18, 9) = 18 × 9
Since the LCM of 18 and 9 = 18
⇒ 18 × GCF(18, 9) = 162
Therefore, the greatest common factor (GCF) = 162/18 = 9.

What is the Least Perfect Square Divisible by 9 and 18?

The least number divisible by 9 and 18 = LCM(9, 18)
LCM of 9 and 18 = 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 9 and 18 = LCM(9, 18) × 2 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.

What are the Methods to Find LCM of 9 and 18?

The commonly used methods to find the LCM of 9 and 18 are:

Prime Factorization Method
Listing Multiples
Division Method

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