LCM of 9 and 33 is 99. The least common multiple of 9 and 33 is determined easily from the common multiples. (9, 18, 27, 36, 45, 54, ….) and (33, 66, 99, 132,….) are the multiples of 9 and 33. Prime factorization method, division method and listing out the multiples discussed here are used to find the LCM of two numbers.
Also read: Least common multiple
What is LCM of 9 and 33?
The answer to this question is 99. The LCM of 9 and 33 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 33, is the smallest positive integer 99 which is divisible by both 9 and 33 with no remainder.
How to Find LCM of 9 and 33?
LCM of 9 and 33 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 33 Using Prime Factorisation Method
The prime factorisation of 9 and 33, respectively, is given by:
9 = 3 x 3 = 3²
33 = 3 x 11 = 3¹ x 11¹
LCM (9, 33) = 99
LCM of 9 and 33 Using Division Method
We’ll divide the numbers (9, 33) by their prime factors to get the LCM of 9 and 33 using the division method (preferably common). The LCM of 9 and 33 is calculated by multiplying these divisors.
|
3 |
9 |
33 |
|
3 |
3 |
11 |
|
11 |
1 |
11 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (9, 33) = 99
LCM of 9 and 33 Using Listing the Multiples
To calculate the LCM of 9 and 33 by listing out the common multiples, list the multiples as shown below
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ….
Multiples of 33 = 33, 66, 99, 132, 165, 198, …..
LCM (9, 33) = 99
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 9 and 33 Solved Examples
Question: If the GCD is 3 and the product of two numbers is 297, what is the value of LCM?
Solution:
Given
GCD = 3
Product = 297
LCM x GCD = Product
LCM = Product/GCD
LCM = 297/3
LCM = 99
Hence, the LCM of 9 and 33 is 99.
Frequently Asked Questions on LCM of 9 and 33
Calculate the LCM of 9 and 33 using the prime factorization method.
To determine the LCM using the prime factorization, we first have to find the prime factors.
9 = 3 x 3
33 = 3 x 11
LCM of 9 and 33 is the product of prime factors raised to the highest exponent among the numbers 9 and 33
LCM of 9 and 33 = 99
If the LCM of 9 and 33 is 99, find the GCF.
LCM x GCF = 9 x 33
Given
LCM of 9 and 33 = 99
99 x GCF = 297
GCF = 297/99 = 3
What is the relation between GCF and LCM of 9 and 33?
The relation between GCF and LCM of 9 and 33 is
LCM x GCF = 9 x 33
LCM x GCF = 297
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