LCM of 8, 12 and 24 is 24. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 8, 12, and 24 is the LCM of 8, 12, and 24. (8, 16, 24, 32, 40…), (12, 24, 36, 48, 60…), and (24, 48, 72, 96, 120…), respectively, are the first few multiples of 8, 12, and 24. There are three typical ways for calculating the LCM of 8, 12, and 24: listing multiples, division method, and prime factorization.
Also read: Least common multiple
What is LCM of 8, 12 and 24?
The answer to this question is 24. The LCM of 8, 12 and 24 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8, 12 and 24, is the smallest positive integer 24 which is divisible by both 8, 12 and 24 with no remainder.
How to Find LCM of 8, 12 and 24?
LCM of 8, 12 and 24 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 12 and 24 Using Prime Factorisation Method
The prime factorisation of 8, 12 and 24, respectively, is given by:
8 = (2 × 2 × 2) = 23,
12 = (2 × 2 × 3) = 22 × 31, and
24 = (2 × 2 × 2 × 3) = 23 × 31
LCM (8, 12, 24) = 24
LCM of 8, 12 and 24 Using Division Method
We’ll divide the numbers (8, 12, 24) by their prime factors to get the LCM of 8, 12 and 24 using the division method (preferably common). The LCM of 8, 12 and 24 is calculated by multiplying these divisors.
| 2 | 8 | 12 | 24 |
| 2 | 4 | 6 | 12 |
| 2 | 2 | 3 | 6 |
| 3 | 1 | 3 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (8, 12, 24) = 24
LCM of 8, 12 and 24 Using Listing the Multiples
To calculate the LCM of 8, 12 and 24 by listing out the common multiples, list the multiples as shown below
| Multiples of 8 | Multiples of 12 | Multiples of 24 |
| 8 | 12 | 24 |
| 16 | 24 | 48 |
| 24 | 36 | 72 |
| 32 | 48 | 96 |
| 40 | 60 | 120 |
The smallest common multiple of 8, 12 and 24 is 24.
Therefore LCM (8, 12, 24) = 24
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LCM of 8, 12 and 24 Solved Example
Question: Find the smallest number that is divisible by 8, 12, 24 exactly.
Solution:
The smallest number that is divisible by 8, 12, and 24 exactly is their LCM.
⇒ Multiples of 8, 12, and 24:
Multiples of 8 = 8, 16, 24, 32, 40, 48, . . . .
Multiples of 12 = 12, 24, 36, 48, 60, 72, . . . .
Multiples of 24 = 24, 48, 72, 96, 120, 144, . . . .
Therefore, the LCM of 8, 12, and 24 is 24.
Frequently Asked Questions on LCM of 8, 12 and 24
What is the LCM of 8, 12 and 24?
List the methods used to find the LCM of 8, 12 and 24.
Which of the following is the LCM of 8, 12, and 24? 24, 12, 81, 105
What is the Least Perfect Square Divisible by 8, 12, and 24?
LCM of 8, 12, and 24 = 2 × 2 × 2 × 3 [Incomplete pair(s): 2, 3] ⇒ Least perfect square divisible by each 8, 12, and 24 = LCM(8, 12, 24) × 2 × 3 = 144 [Square root of 144 = √144 = ±12] Therefore, 144 is the required number.
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