LCM of 8 and 21 is 168. LCM is the method used to get the smallest common multiple which lies between the numbers 8 and 21. Least common multiples of 8 and 21 can be found by knowing the common multiples. (8, 16, 24, 32, 40, 48, 56, ….) and (21, 42, 63, 84, 105, ….) are the multiples of 8 and 21. The LCM of two numbers is calculated using certain methods like listing the multiples, prime factorization and division.
Also read: Least common multiple
What is LCM of 8 and 21?
The answer to this question is 168. The LCM of 8 and 21 as per certain methods is provided in this article for your reference. The LCM of 8 and 21, is the smallest integer 168 divisible by 8 and 21 with remainder as zero.
How to Find LCM of 8 and 21?
LCM of 8 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8 and 21 Using Prime Factorisation Method
The prime factorisation of 8 and 21 can be written as:
8 = 2 x 2 x 2 = 2³
21 = 3 x 7 = 3¹ x 7¹
LCM (8, 21) = 168
LCM of 8 and 21 Using Division Method
The numbers (8, 21) should be divided by their prime factors to find the LCM value. The LCM of 8 and 21 is obtained by multiplying these divisors.
|
2 |
8 |
21 |
|
2 |
4 |
21 |
|
2 |
2 |
21 |
|
3 |
1 |
21 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (8, 21) = 168
LCM of 8 and 21 Using Listing the Multiples
To calculate the LCM of 8 and 21 by listing out the common multiples, list the multiples as shown below
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . . ., 136, 144, 152, 160, 168, . . . .
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . ., 84, 105, 126, 147, 168, . . .
LCM (8, 21) = 168
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 8 and 21 Solved Examples
Question: Determine the smallest number exactly divisible by 8 and 21.
Solution:
We know that
LCM is the smallest number exactly divisible by 8 and 21.
(8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . . ., 136, 144, 152, 160, 168, . . . .) are the multiples of 8
(21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . ., 84, 105, 126, 147, 168, . . .) are the multiples of 21
Hence, the LCM of 8 and 21 is 168.
Frequently Asked Questions on LCM of 8 and 21
What methods can we use to find the LCM of 8 and 21?
The methods which we can use to find the LCM of 8 and 21 are
Prime Factorisation
Division method
Listing the multiples
By using prime factorisation, determine the LCM of 8 and 21.
To find the LCM, the factors must be known
8 = 2 x 2 x 2
21 = 3 x 7
LCM is the product of prime factors raised to the highest exponent among 8 and 21.
LCM of 8, 21 = 168
Find the GCF if the LCM of 8 and 21 is 168.
LCM x GCF = 8 x 21
As the LCM = 168
168 x GCF = 168
GCF = 168/168 = 1
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