LCM of 24 and 56 is 168. The number evenly divisible by 24 and 56 provides the value of LCM. Least common multiples of 24 and 56 are found by noting down the common multiples. (24, 48, 72, 96, 120, ….) and (56, 112, 168, 224, 280, 336,….) are the multiples of 24 and 56. The LCM of two numbers using the prime factorization, division and by listing the multiples are provided in this article in an understanding manner for the benefit of students.
Also read: Least common multiple
What is LCM of 24 and 56?
The answer to this question is 168. The LCM of 24 and 56 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 56, is the smallest positive integer 168 which is divisible by both 24 and 56 with no remainder.
How to Find LCM of 24 and 56?
LCM of 24 and 56 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24 and 56 Using Prime Factorisation Method
The prime factorisation of 24 and 56, respectively, is given by:
24 = 2 × 2 × 2 × 3 = 2³ × 3¹
56 = 2 × 2 × 2 × 7 = 2³× 7¹
LCM (24, 56) = 168
LCM of 24 and 56 Using Division Method
We’ll divide the numbers (24, 56) by their prime factors to get the LCM of 24 and 56 using the division method (preferably common). The LCM of 24 and 56 is calculated by multiplying these divisors.
|
2 |
24 |
56 |
|
2 |
12 |
28 |
|
2 |
6 |
14 |
|
3 |
3 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (24, 56) = 168
LCM of 24 and 56 Using Listing the Multiples
To calculate the LCM of 24 and 56 by listing out the common multiples, list the multiples as shown below
|
Multiples of 24 |
Multiples of 56 |
|
24 |
56 |
|
48 |
112 |
|
72 |
168 |
|
96 |
224 |
|
120 |
280 |
|
144 |
336 |
|
168 |
392 |
LCM (24, 56) = 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 24 and 56 Solved Examples
Question: What is the smallest number which is exactly divisible by 24 and 56?
Solution:
We know that
The smallest number which is exactly divisible by 24 and 56 is the LCM.
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, ….
Multiples of 56 = 56, 112, 168, 224, 280, 336, 392,….
Hence, the LCM of 24 and 56 is 168.
Frequently Asked Questions on LCM of 24 and 56
What is the LCM of 24 and 56 using the prime factorization method?
To find the LCM using the prime factorization, we should know the prime factors.
24 = 2 × 2 × 2 × 3 = 2³ × 3¹
56 = 2 × 2 × 2 × 7 = 2³× 7¹
LCM of 24 and 56 is the product of prime factors raised to the highest exponent among the numbers 24 and 56
LCM of 24 and 56 = 168
If the LCM of 24 and 56 is 168, find the GCF.
LCM × GCF = 24 × 56
Given
LCM of 24 and 56 = 168
168 × GCF = 1344
GCF = 1344/168 = 8
Show the relation between GCF and LCM of 24 and 56.
The relation between GCF and LCM of 24 and 56 is
LCM × GCF = 24 × 56
LCM × GCF = 1344
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