LCM of 9, 14 and 21 is 126. The value which is divisible exactly by the numbers 9, 14 and 21 is the LCM value. From the common multiples you will be able to find the least common multiple of 9, 14 and 21. The multiples of 9 are (9, 18, 27, 36, 45, ….), the multiples of 14 are (14, 28, 42, 56, 70, …..) and the multiples of 21 are (21, 42, 63, 84, 105, ….) respectively. The methods to find the LCM of the numbers are prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 9, 14 and 21?
The answer to this question is 126. The LCM of 9, 14 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9, 14 and 21, is the smallest positive integer 126 which is divisible by both 9, 14 and 21 with no remainder.
How to Find LCM of 9, 14 and 21?
LCM of 9, 14 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9, 14 and 21 Using Prime Factorisation Method
The prime factorisation of 9, 14 and 21, respectively, is given by:
9 = 3 x 3 = 3²
14 = 2 x 7 = 2¹ x 7¹
21 = 3 x 7 = 3¹ x 7¹
LCM (9, 14, 21) = 126
LCM of 9, 14 and 21 Using Division Method
We’ll divide the numbers (9, 14, 21) by their prime factors to get the LCM of 9, 14 and 21 using the division method (preferably common). The LCM of 9, 14 and 21 is calculated by multiplying these divisors.
|
2 |
9 |
14 |
21 |
|
3 |
9 |
7 |
21 |
|
3 |
3 |
7 |
7 |
|
7 |
1 |
7 |
7 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (9, 14, 21) = 126
LCM of 9, 14 and 21 Using Listing the Multiples
To calculate the LCM of 9, 14 and 21 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, 108, 117, 126, …..
Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126, ……
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, …….
LCM (9, 14, 21) = 126
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LCM of 9, 14 and 21 Solved Examples
Question: In the numbers 21, 126, 110, 11, which is the LCM of 9, 14 and 21?
Solution:
LCM is the smallest common multiple divisible evenly by the given numbers
126 satisfies this condition
Hence, the LCM is 126.
Frequently Asked Questions on LCM of 9, 14 and 21
If the LCM of 9, 14 and 21 is 126, what is its GCF?
We know that
LCM x GCF = 9 x 14 x 21
As LCM (9, 14, 21) is 126
126 x GCF = 2646
GCF = 2646/126 = 21
Find the LCM of 9, 14 and 21.
Show the relation between GCF and LCM of 9, 14 and 21.
The relation between GCF and LCM of 9, 14 and 21 is
LCM x GCF = 9 x 14 x 21
LCM x GCF = 2646
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