A day full of math games & activities. Find one near you.

LCM of 4 and 9

LCM of 4 and 9 is the smallest number among all common multiples of 4 and 9. The first few multiples of 4 and 9 are (4, 8, 12, 16, 20, 24, 28, . . . ) and (9, 18, 27, 36, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 9 - by prime factorization, by listing multiples, and by division method.

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

What is the LCM of 4 and 9?

Answer: LCM of 4 and 9 is 36.

Explanation:

The LCM of two non-zero integers, x(4) and y(9), is the smallest positive integer m(36) that is divisible by both x(4) and y(9) without any remainder.

Methods to Find LCM of 4 and 9

The methods to find the LCM of 4 and 9 are explained below.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 4 and 9 by Listing Multiples

To calculate the LCM of 4 and 9 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, 28, . . . ) and 9 (9, 18, 27, 36, . . . . )
Step 2: The common multiples from the multiples of 4 and 9 are 36, 72, . . .
Step 3: The smallest common multiple of 4 and 9 is 36.

∴ The least common multiple of 4 and 9 = 36.

LCM of 4 and 9 by Prime Factorization

Prime factorization of 4 and 9 is (2 × 2) = 2² and (3 × 3) = 3² respectively. LCM of 4 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² = 36.
Hence, the LCM of 4 and 9 by prime factorization is 36.

LCM of 4 and 9 by Division Method

To calculate the LCM of 4 and 9 by the division method, we will divide the numbers(4, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 9.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 9. Write this prime number(2) on the left of the given numbers(4 and 9), separated as per the ladder arrangement.
Step 2: If any of the given numbers (4, 9) 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 4 and 9 is the product of all prime numbers on the left, i.e. LCM(4, 9) by division method = 2 × 2 × 3 × 3 = 36.

☛ Also Check:

LCM of 4 and 9 Examples

Example 1: Find the smallest number that is divisible by 4 and 9 exactly.

Solution:

The smallest number that is divisible by 4 and 9 exactly is their LCM.
⇒ Multiples of 4 and 9:
- Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, . . . .
- Multiples of 9 = 9, 18, 27, 36, 45, 54, . . . .
Therefore, the LCM of 4 and 9 is 36.
Example 2: The GCD and LCM of two numbers are 1 and 36 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 = (1 × 36)/9
⇒ m = 4
Therefore, the other number is 4.
Example 3: The product of two numbers is 36. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 36
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 36/1
Therefore, the LCM is 36.
The probable combination for the given case is LCM(4, 9) = 36.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on LCM of 4 and 9

What is the LCM of 4 and 9?

The LCM of 4 and 9 is 36. To find the least common multiple (LCM) of 4 and 9, we need to find the multiples of 4 and 9 (multiples of 4 = 4, 8, 12, 16 . . . . 36; multiples of 9 = 9, 18, 27, 36) and choose the smallest multiple that is exactly divisible by 4 and 9, i.e., 36.

How to Find the LCM of 4 and 9 by Prime Factorization?

To find the LCM of 4 and 9 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (9 = 3 × 3). LCM of 4 and 9 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 9.
⇒ LCM of 4, 9 = 2² × 3² = 36.

What is the Relation Between GCF and LCM of 4, 9?

The following equation can be used to express the relation between GCF and LCM of 4 and 9, i.e. GCF × LCM = 4 × 9.

If the LCM of 9 and 4 is 36, Find its GCF.

LCM(9, 4) × GCF(9, 4) = 9 × 4
Since the LCM of 9 and 4 = 36
⇒ 36 × GCF(9, 4) = 36
Therefore, the greatest common factor (GCF) = 36/36 = 1.

What is the Least Perfect Square Divisible by 4 and 9?

The least number divisible by 4 and 9 = LCM(4, 9)
LCM of 4 and 9 = 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 4 and 9 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.

Download FREE Study Materials

LCM and GCF

Math worksheets and
visual curriculum