LCM of 4 and 9 is 36. The number which is evenly divisible by the two numbers, 4 and 9 gives you the LCM value. Least common multiples of 4 and 9 can be obtained from the common multiples. (4, 8, 12, 16, 20, 24, ….) and (9, 18, 27, 36, 45, 54,….) are the multiples of 4 and 9. The LCM of two numbers using prime factorization, division and by listing the multiples are given here for a good conceptual knowledge.
Also read: Least common multiple
What is LCM of 4 and 9?
The answer to this question is 36. The LCM of 4 and 9 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4 and 9, is the smallest positive integer 36 which is divisible by both 4 and 9 with no remainder.
How to Find LCM of 4 and 9?
LCM of 4 and 9 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4 and 9 Using Prime Factorisation Method
The prime factorisation of 4 and 9, respectively, is given by:
4 = 2 x 2 = 2²
9 = 3 x 3 = 3²
LCM (4, 9) = 36
LCM of 4 and 9 Using Division Method
We’ll divide the numbers (4, 9) by their prime factors to get the LCM of 4 and 9 using the division method (preferably common). The LCM of 4 and 9 is calculated by multiplying these divisors.
| 2 | 4 | 9 |
| 2 | 2 | 9 |
| 3 | 1 | 9 |
| 3 | 1 | 3 |
| 1 | 1 |
No further division can be done.
Hence, LCM (4, 9) = 36
LCM of 4 and 9 Using Listing the Multiples
To calculate the LCM of 4 and 9 by listing out the common multiples, list the multiples as shown below
| Multiples of 4 | Multiples of 9 |
| 4 | 9 |
| 8 | 18 |
| 12 | 27 |
| 16 | 36 |
| 20 | 45 |
| 24 | 54 |
| 28 | |
| 36 | |
| 40 |
LCM (4, 9) = 36
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LCM of 4 and 9 Solved Examples
Question: What is the smallest number exactly divisible by 4 and 9?
Solution:
We know that
The smallest number which is exactly divisible by 4 and 9 is the LCM.
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, …..
Multiples of 9 = 9, 18, 27, 36, 45, 54, ….
Hence, the LCM of 4 and 9 is 36.
Frequently Asked Questions on LCM of 4 and 9
Calculate the LCM of 4 and 9 using the prime factorization method.
To determine the LCM using the prime factorization, we first have to find the prime factors.
4 = 2 x 2
9 = 3 x 3
LCM of 4 and 9 is the product of prime factors raised to the highest exponent among the numbers 4 and 9
LCM of 4 and 9 = 2² x 3² = 36
If the LCM of 4 and 9 is 36, find the GCF.
LCM x GCF = 4 x 9
Given
LCM of 4 and 9 = 36
36 x GCF = 36
GCF = 36/36 = 1
What is the relation between GCF and LCM of 4 and 9?
The relation between GCF and LCM of 4 and 9 is
LCM x GCF = 4 x 9
LCM x GCF = 36
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