LCM of 24 and 28 is 168. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 24 and 28 is the smallest number among all common multiples of 24 and 28. The first few multiples of 24 and 28 are (24, 48, 72, 96, 120, . . . ) and (28, 56, 84, 112, 140, 168, 196, . . . ) respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 24 and 28?
The answer to this question is 168. The LCM of 24 and 28 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 28, is the smallest positive integer 168 which is divisible by both 24 and 28 with no remainder.
How to Find LCM of 24 and 28?
LCM of 24 and 28 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24 and 28 Using Prime Factorisation Method
The prime factorisation of 24 and 28, respectively, is given by:
24 = (2 × 2 × 2 × 3) = 23 × 31 and
28 = (2 × 2 × 7) = 22 × 71
LCM (24, 28) = 168
LCM of 24 and 28 Using Division Method
We’ll divide the numbers (24, 28) by their prime factors to get the LCM of 24 and 28 using the division method (preferably common). The LCM of 24 and 28 is calculated by multiplying these divisors.
| 2 | 24 | 28 |
| 2 | 12 | 14 |
| 2 | 6 | 7 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (24, 28) = 168
LCM of 24 and 28 Using Listing the Multiples
To calculate the LCM of 24 and 28 by listing out the common multiples, list the multiples as shown below.
| Multiples of 24 | Multiples of 28 |
| 24 | 28 |
| 48 | 56 |
| 72 | 84 |
| 96 | 112 |
| 120 | 140 |
| 144 | 168 |
| 168 | 196 |
The smallest common multiple of 24 and 28 is 168.
Therefore LCM (24, 28) = 168
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LCM of 24 and 28 Solved Example
Question: The product of two numbers is 672. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 672
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 672/4
Therefore, the LCM is 168.
The probable combination for the given case is LCM(24, 28) = 168.
Frequently Asked Questions on LCM of 24 and 28
What is the LCM of 24 and 28?
The LCM of 24 and 28 is 168. To find the least common multiple (LCM) of 24 and 28, we need to find the multiples of 24 and 28 (multiples of 24 = 24, 48, 72, 96 . . . . 168; multiples of 28 = 28, 56, 84, 112 . . . . 168) and choose the smallest multiple that is exactly divisible by 24 and 28, i.e., 168./div>
List the methods used to find the LCM of 24 and 28.
Find the smallest number that is divisible by 24 and 28 exactly.
⇒ Multiples of 24 and 28:
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, . . . .
Multiples of 28 = 28, 56, 84, 112, 140, 168, . . . .
Therefore, the LCM of 24 and 28 is 168.
If the LCM of 28 and 24 is 168, Find its GCF.
Since the LCM of 28 and 24 = 168
⇒ 168 × GCF(28, 24) = 672
Therefore, the greatest common factor = 672/168 = 4.
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