LCM of 21 and 24 is 168. The number which equally divides 21 and 24 provides the LCM. The common multiples of the two numbers will assist you in obtaining the least common multiple of 21 and 24. The multiples of 21 are (21, 42, 63, 84, 105, 126, 147, ….) and the multiples of 24 are (24, 48, 72, 96, 120, 144, …..) respectively. For a precise knowledge of the LCM concept and prime factorisation method, division method and listing of the multiples go through the materials given at BYJU’S.
Also read: Least common multiple
What is LCM of 21 and 24?
The answer to this question is 168. The LCM of 21 and 24 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 21 and 24, is the smallest positive integer 168 which is divisible by both 21 and 24 with no remainder.
How to Find LCM of 21 and 24?
LCM of 21 and 24 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 21 and 24 Using Prime Factorisation Method
The prime factorisation of 21 and 24, respectively, is given by:
21 = 3 x 7 = 3¹ x 7¹
24 = 2 x 2 x 2 x 3 = 2³ x 3¹
LCM (21, 24) = 168
LCM of 21 and 24 Using Division Method
We’ll divide the numbers (21, 24) by their prime factors to get the LCM of 21 and 24 using the division method (preferably common). The LCM of 21 and 24 is calculated by multiplying these divisors.
|
2 |
21 |
24 |
|
2 |
21 |
12 |
|
2 |
21 |
6 |
|
3 |
21 |
3 |
|
7 |
7 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (21, 24) = 168
LCM of 21 and 24 Using Listing the Multiples
To calculate the LCM of 21 and 24 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 21 |
Multiples of 24 |
|
21 |
24 |
|
42 |
48 |
|
63 |
72 |
|
84 |
96 |
|
105 |
120 |
|
126 |
144 |
|
147 |
168 |
|
168 |
192 |
|
189 |
216 |
|
210 |
240 |
LCM (21, 24) = 168
Related Articles
Video Lesson on Applications of LCM
LCM of 21 and 24 Solved Examples
Find the smallest number divisible by 21 and 24 exactly.
Solution:
The smallest number divisible by 21 and 24 exactly is LCM.
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, . . . .
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, . . . .
Therefore, the LCM of 21 and 24 is 168.
Frequently Asked Questions on LCM of 21 and 24
Find the GCF if the LCM of 21 and 24 is 168.
We know that
LCM x GCF = 21 x 24
As LCM (21, 24) is 168
168 x GCF = 504
GCF = 504/168 = 3
Find the LCM of 21 and 24.
The LCM of 21 and 24 is 168. The multiples of 21 and 24 has to be found first to get the LCM value
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, . . . .
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, . . . .
The smallest multiple exactly divisible by 21 and 24 is 168.
Show the relation between GCF and LCM of 21 and 24.
The relation between GCF and LCM of 21 and 24 is:
LCM x GCF = 21 x 24
LCM x GCF =504
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