LCM of 9 and 27 is 72. Among all common multiples of 9 and 27, the LCM of 9 and 27 is the smallest number. (9, 18, 27, 36, 45, 54, etc.) and (27, 54, 81, 108, etc.) are the first few multiples of 9 and 27, respectively. Prime factorization, listing multiples, and division are the three most frequent methods for determining the LCM of 9 and 27. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 9 and 27?
The answer to this question is 27. The LCM of 9 and 27 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 27, is the smallest positive integer 27 which is divisible by both 9 and 27 with no remainder.
How to Find LCM of 9 and 27?
LCM of 9 and 27 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 27 Using Prime Factorisation Method
The prime factorisation of 9 and 27, respectively, is given by:
9 = (3 × 3) = 32 and
27 = (3 × 3 × 3) = 33
LCM (24, 36) = 72
LCM of 9 and 27 Using Division Method
We’ll divide the numbers (9, 27) by their prime factors to get the LCM of 9 and 27 using the division method (preferably common). The LCM of 9 and 27 is calculated by multiplying these divisors.
| 3 | 9 | 27 |
| 3 | 3 | 9 |
| 3 | 1 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 27) = 27
LCM of 9 and 27 Using Listing the Multiples
To calculate the LCM of 9 and 27 by listing out the common multiples, list the multiples as shown below
| Multiples of 9 | Multiples of 27 |
| 9 | 27 |
| 18 | 54 |
| 27 | 81 |
| 36 | – |
| 45 | – |
The smallest common multiple of 9 and 27 is 27.
Therefore LCM (9, 27) = 27
Related Articles
Video Lesson on Applications of LCM
LCM of 9 and 27 Solved Examples
The GCD and LCM of two numbers are 9 and 27 respectively. If one number is 27, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 27 × p
⇒ p = (GCD × LCM)/27
⇒ p = (9 × 27)/27
⇒ p = 9
Therefore, the other number is 9.
Frequently Asked Questions on LCM of 9 and 27
What is the LCM of 9 and 27?
List the methods used to find the LCM of 9 and 27.
If the LCM of 27 and 9 is 27, Find its GCF.
Since the LCM of 27 and 9 = 27
⇒ 27 × GCF(27, 9) = 243
Therefore, the greatest common factor (GCF) = 243/27 = 9.
What is the Least Perfect Square Divisible by 9 and 27?
LCM of 9 and 27 = 3 × 3 × 3 [Incomplete pair(s): 3] ⇒ Least perfect square divisible by each 9 and 27 = LCM(9, 27) × 3 = 81 [Square root of 81 = √81 = ±9] Therefore, 81 is the required number.
Comments