LCM of 2 and 9 is 18. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. The smallest number among all common multiples of 2 and 9 is the LCM of 2 and 9. (2, 4, 6, 8, 10, etc.) and (9, 18, 27, 36, etc.) are the first few multiples of 2 and 9. To find the LCM of 2 and 9, you can use one of three methods: listing multiples, prime factorization, or the division method.
Also read: Least common multiple
What is LCM of 2 and 9?
The answer to this question is 18. The LCM of 2 and 9 using various methods are shown in this article for your reference. The LCM of two non-zero integers, 2 and 9, is the smallest positive integer 18 which is divisible by both 2 and 9 with no remainder.
How to Find LCM of 2 and 9?
LCM of 2 and 9 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 2 and 9 Using Prime Factorisation Method
The prime factorisation of 2 and 9, respectively, is given by:
(2) = 21 and (3 × 3) = 32
LCM (2, 9) = 18
LCM of 2 and 9 Using Division Method
We’ll divide the numbers (2, 9) by their prime factors to get the LCM of 2 and 9 using the division method (preferably common). The LCM of 2 and 9 is calculated by multiplying these divisors.
2 | 2 | 9 |
3 | 1 | 9 |
3 | 1 | 3 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (2, 9) = 18
LCM of 2 and 9 Using Listing the Multiples
To calculate the LCM of 2 and 9 by listing out the common multiples, list the multiples as shown below
Multiples of 2 | Multiples of 9 |
2 | 9 |
4 | 18 |
6 | 27 |
8 | 36 |
10 | 45 |
12 | 54 |
14 | 63 |
16 | 72 |
18 | 84 |
The smallest common multiple of 2 and 9 is 18.
LCM (2, 9) = 18
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Video Lesson on Applications of LCM
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LCM of 2 and 9 Solved Example
Question: The GCD and LCM of two numbers are 1 and 18 respectively. If one number is 9, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 9 × b
⇒ b = (GCD × LCM)/9
⇒ b = (1 × 18)/9
⇒ b = 2
Therefore, the other number is 2.
Frequently Asked Questions on LCM of 2 and 9
What is the LCM of 2 and 9?
List the methods used to find the LCM of 2 and 9.
If the LCM of 9 and 2 is 18, Find its GCF.
Since the LCM of 9 and 2 = 18
⇒ 18 × GCF(9, 2) = 18
Therefore, the greatest common factor = 18/18 = 1.
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