LCM of 3 and 9 is 9. The number evenly divisible by the given numbers provides the LCM. Of the multiples which are common, the least common multiple of 3 and 9 can be found. The multiples of 3 are (3, 6, 9, 12, 15, 18, 21, ….) and the multiples of 9 are (9, 18, 27, 36, 45, 54, ….) respectively. The methods used to calculate the LCM are prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 3 and 9?
The answer to this question is 9. The LCM of 3 and 9 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 9, is the smallest positive integer 9 which is divisible by both 3 and 9 with no remainder.
How to Find LCM of 3 and 9?
LCM of 3 and 9 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3 and 9 Using Prime Factorisation Method
The prime factorisation of 3 and 9, respectively, is given by:
3 = 3¹
9 = 3 x 3 = 3²
LCM (3, 9) = 9
LCM of 3 and 9 Using Division Method
We’ll divide the numbers (3, 9) by their prime factors to get the LCM of 3 and 9 using the division method (preferably common). The LCM of 3 and 9 is calculated by multiplying these divisors.
| 3 | 3 | 9 |
| 3 | 1 | 3 |
| 1 | 1 |
No further division can be done.
Hence, LCM (3, 9) = 9
LCM of 3 and 9 Using Listing the Multiples
To calculate the LCM of 3 and 9 by listing out the common multiples, list the multiples as shown below
| Multiples of 3 | Multiples of 9 |
| 3 | 9 |
| 6 | 18 |
| 9 | 27 |
| 12 | 36 |
| 15 | 45 |
LCM (3, 9) = 9
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Video Lesson on Applications of LCM
LCM of 3 and 9 Solved Examples
Question: The LCM and GCD of two numbers are 9 and 3, respectively. If one number is 9, what is the other number?
Solution:
Consider the number as z
We know that
GCD x LCM = 9 x z
z = (GCD x LCM)/9
Substituting the values
z = (9 x 3)/9
z = 3
Hence, the other number is 3.
Frequently Asked Questions on LCM of 3 and 9
If the LCM of 3 and 9is 9, what is its GCF?
We know that
LCM x GCF = 3 x 9
As LCM (3, 9) is 9
9 x GCF = 27
GCF = 27/9 = 3
Find the LCM of 3 and 9.
The LCM of 3 and 9 is 9. To find the LCM, we first should understand the multiples of 3 and 9
Multiples of 3 = 3, 6, 9, 12, 15, 18, ……
Multiples of 9 = 9, 18, 27, 36, 45, 54, ….
The smallest multiple exactly divisible by 3 and 9 is 9.
Show the relation between GCF and LCM of 3 and 9.
The relation between GCF and LCM of 3 and 9 is
LCM x GCF = 3 x 9
LCM x GCF = 27
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