LCM of 4, 8 and 12 is 24. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Least common multiple of 4, 8 and 12 is the smallest number we get among the common multiples. The first few multiples of 4, 8, and 12 are (4, 8, 12, 16, 20 . . .), (8, 16, 24, 32, 40 . . .), and (12, 24, 36, 48, 60 . . .) 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 4, 8 and 12?
The answer to this question is 24. The LCM of 4, 8 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4, 8 and 12, is the smallest positive integer 24 which is divisible by both 4, 8 and 12 with no remainder.
How to Find LCM of 4, 8 and 12?
LCM of 4, 8 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4, 8 and 12 Using Prime Factorisation Method
The prime factorisation of 4, 8 and 12, respectively, is given by:
4 = (2 × 2) = 22,
8 = (2 × 2 × 2) = 23, and
12 = (2 × 2 × 3) = 22 × 31
LCM (4, 8, 12) = 24
LCM of 4, 8 and 12 Using Division Method
We’ll divide the numbers (4, 8, 12) by their prime factors to get the LCM of 4, 8 and 12 using the division method (preferably common). The LCM of 4, 8 and 12 is calculated by multiplying these divisors.
| 2 | 4 | 8 | 12 |
| 2 | 2 | 4 | 6 |
| 2 | 1 | 2 | 3 |
| 3 | 1 | 1 | 3 |
| 1 | 1 | 1 |
No further division can be done.
Hence, LCM (4, 8, 12) = 24
LCM of 4, 8 and 12 Using Listing the Multiples
To calculate the LCM of 4, 8 and 12 by listing out the common multiples, list the multiples as shown below
| Multiples of 4 | Multiples of 8 | Multiples of 12 |
| 4 | 8 | 12 |
| 8 | 16 | 24 |
| 12 | 24 | 36 |
| 16 | 32 | 48 |
| 20 | 40 | 60 |
| 24 | 48 | 72 |
The smallest common multiple of 4, 8 and 12 is 24.
Therefore LCM (4, 8, 12) = 24
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LCM of 4, 8 and 12 Solved Example
Find the smallest number that is divisible by 4, 8, 12 exactly.
Solution:
The smallest number that is divisible by 4, 8, and 12 exactly is their LCM.
⇒ Multiples of 4, 8, and 12:
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, . . . .
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, . . . .
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, . . . .
Therefore, the LCM of 4, 8, and 12 is 24.
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