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LCM of 9 and 36

LCM of 9 and 36 is the smallest number among all common multiples of 9 and 36. The first few multiples of 9 and 36 are (9, 18, 27, 36, 45, . . . ) and (36, 72, 108, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 36 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 9 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 9 and 36?

Answer: LCM of 9 and 36 is 36.

Explanation:

The LCM of two non-zero integers, x(9) and y(36), is the smallest positive integer m(36) that is divisible by both x(9) and y(36) without any remainder.

Methods to Find LCM of 9 and 36

Let's look at the different methods for finding the LCM of 9 and 36.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 9 and 36 by Division Method

To calculate the LCM of 9 and 36 by the division method, we will divide the numbers(9, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 36.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 36. Write this prime number(2) on the left of the given numbers(9 and 36), separated as per the ladder arrangement.
Step 2: If any of the given numbers (9, 36) 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 36 is the product of all prime numbers on the left, i.e. LCM(9, 36) by division method = 2 × 2 × 3 × 3 = 36.

LCM of 9 and 36 by Prime Factorization

Prime factorization of 9 and 36 is (3 × 3) = 3² and (2 × 2 × 3 × 3) = 2² × 3² respectively. LCM of 9 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² = 36.
Hence, the LCM of 9 and 36 by prime factorization is 36.

LCM of 9 and 36 by Listing Multiples

To calculate the LCM of 9 and 36 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, 45, . . . ) and 36 (36, 72, 108, 144, . . . . )
Step 2: The common multiples from the multiples of 9 and 36 are 36, 72, . . .
Step 3: The smallest common multiple of 9 and 36 is 36.

∴ The least common multiple of 9 and 36 = 36.

☛ Also Check:

LCM of 9 and 36 Examples

Example 1: Verify the relationship between GCF and LCM of 9 and 36.

Solution:

The relation between GCF and LCM of 9 and 36 is given as,
LCM(9, 36) × GCF(9, 36) = Product of 9, 36
Prime factorization of 9 and 36 is given as, 9 = (3 × 3) = 3² and 36 = (2 × 2 × 3 × 3) = 2² × 3²
LCM(9, 36) = 36
GCF(9, 36) = 9
LHS = LCM(9, 36) × GCF(9, 36) = 36 × 9 = 324
RHS = Product of 9, 36 = 9 × 36 = 324
⇒ LHS = RHS = 324
Hence, verified.
Example 2: The product of two numbers is 324. If their GCD is 9, what is their LCM?

Solution:

Given: GCD = 9
product of numbers = 324
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 324/9
Therefore, the LCM is 36.
The probable combination for the given case is LCM(9, 36) = 36.
Example 3: The GCD and LCM of two numbers are 9 and 36 respectively. If one number is 36, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 36 × b
⇒ b = (GCD × LCM)/36
⇒ b = (9 × 36)/36
⇒ b = 9
Therefore, the other number is 9.

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FAQs on LCM of 9 and 36

What is the LCM of 9 and 36?

The LCM of 9 and 36 is 36. To find the least common multiple of 9 and 36, we need to find the multiples of 9 and 36 (multiples of 9 = 9, 18, 27, 36; multiples of 36 = 36, 72, 108, 144) and choose the smallest multiple that is exactly divisible by 9 and 36, i.e., 36.

How to Find the LCM of 9 and 36 by Prime Factorization?

To find the LCM of 9 and 36 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (36 = 2 × 2 × 3 × 3). LCM of 9 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 36.
⇒ LCM of 9, 36 = 2² × 3² = 36.

If the LCM of 36 and 9 is 36, Find its GCF.

LCM(36, 9) × GCF(36, 9) = 36 × 9
Since the LCM of 36 and 9 = 36
⇒ 36 × GCF(36, 9) = 324
Therefore, the greatest common factor (GCF) = 324/36 = 9.

Which of the following is the LCM of 9 and 36? 11, 3, 40, 36

The value of LCM of 9, 36 is the smallest common multiple of 9 and 36. The number satisfying the given condition is 36.

What is the Relation Between GCF and LCM of 9, 36?

The following equation can be used to express the relation between GCF and LCM of 9 and 36, i.e. GCF × LCM = 9 × 36.

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