LCM of 4, 6 and 12 is 12. The smallest number among all common multiples of 4, 6, and 12 is the LCM of 4, 6, and 12. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. (4, 8, 12, 16, 20, etc. ), (6, 12, 18, 24, 30, etc. ), and (12, 24, 36, 48, 60, etc.) are the first few multiples of 4, 6, and 12. There are three typical ways for calculating the LCM of 4, 6, and 12: naming multiples, prime factorization, and division.
Also read: Least common multiple
What is LCM of 4, 6 and 12?
The answer to this question is 12. The LCM of 4, 6 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 4, 6 and 12, is the smallest positive integer 12 which is divisible by both 4, 6 and 12 with no remainder.
How to Find LCM of 4, 6 and 12?
LCM of 4, 6 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 4, 6 and 12 Using Prime Factorisation Method
The prime factorisation of 4, 6 and 12, respectively, is given by:
4 = (2 × 2) = 22,
6 = (2 × 3) = 21 × 31, and
12 = (2 × 2 × 3) = 22 × 31
LCM (4, 6, 12) = 12
LCM of 4, 6 and 12 Using Division Method
We’ll divide the numbers (4, 6, 12) by their prime factors to get the LCM of 4, 6 and 12 using the division method (preferably common). The LCM of 4, 6 and 12 is calculated by multiplying these divisors.
| 2 | 4 | 6 | 12 |
| 2 | 2 | 3 | 6 |
| 3 | 1 | 3 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (4, 6, 12) = 12
LCM of 4, 6 and 12 Using Listing the Multiples
To calculate the LCM of 4, 6 and 12 by listing out the common multiples, list the multiples as shown below
| Multiples of 4 | Multiples of 6 | Multiples of 12 |
| 4 | 6 | 12 |
| 8 | 12 | 24 |
| 12 | 18 | 36 |
| 16 | 24 | 48 |
| 20 | 30 | 60 |
The smallest common multiple of 4, 6 and 12 is 12.
Therefore LCM (4, 6, 12) = 12
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LCM of 4, 6 and 12 Solved Example
Find the smallest number that is divisible by 4, 6, 12 exactly.
Solution:
The smallest number that is divisible by 4, 6, and 12 exactly is their LCM.
⇒ Multiples of 4, 6, and 12:
Multiples of 4 = 4, 8, 12, 16, 20, . . . .
Multiples of 6 = 6, 12, 18, 24, 30, . . . .
Multiples of 12 = 12, 24, 36, 48, 60, . . . .
Therefore, the LCM of 4, 6, and 12 is 12.
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