LCM of 2, 4 and 6 is 12. The value evenly divisible by the numbers 2, 4 and 6 is the LCM. The multiples common among the two numbers will assist you to know the least common multiple of 2, 4 and 6. The multiples of 2 are (2, 4, 6, 8, 10, ….), multiples of 4 are (4, 8, 12, 16, 20, …..) and the multiples of 6 are (6, 12, 18, 24, 30, ….) respectively. Students can get the LCM using the prime factorisation method, division method and by listing out the multiples of 2, 4 and 6.
Also read: Least common multiple
What is LCM of 2, 4 and 6?
The answer to this question is 12. The LCM of 2, 4 and 6 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 2, 4 and 6, is the smallest positive integer 12 which is divisible by both 2, 4 and 6 with no remainder.
How to Find LCM of 2, 4 and 6?
LCM of 2, 4 and 6 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 2, 4 and 6 Using Prime Factorisation Method
The prime factorisation of 2, 4 and 6, respectively, is given by:
2 = 2 = 2¹
4 = 2 x 2 = 2²
6 = 2 x 3 = 2¹ x 3¹
LCM (2, 4, 6) = 12
LCM of 2, 4 and 6 Using Division Method
We’ll divide the numbers (2, 4, 6) by their prime factors to get the LCM of 2, 4 and 6 using the division method (preferably common). The LCM of 2, 4 and 6 is calculated by multiplying these divisors.
| 2 | 2 | 4 | 6 |
| 2 | 1 | 2 | 3 |
| 3 | 1 | 1 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (2, 4, 6) = 12
LCM of 2, 4 and 6 Using Listing the Multiples
To calculate the LCM of 2, 4 and 6 by listing out the common multiples, list the multiples as shown below.
| Multiples of 2 | Multiples of 4 | Multiples of 6 |
| 2 | 4 | 6 |
| 4 | 8 | 12 |
| 6 | 12 | 18 |
| 8 | 16 | 24 |
| 10 | 20 | 30 |
| 12 | 24 | 36 |
| 14 | 28 | 42 |
| 16 | 32 | 48 |
LCM (2, 4, 6) = 12
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Video Lesson on Applications of LCM
LCM of 2, 4 and 6 Solved Example
Question: What is the smallest number divisible by 2, 4 and 6?
Solution:
The smallest number divisible by 2, 4 and 6 exactly is LCM.
Multiples of 2 = 2, 4, 6, 8, 10, ….
Multiples of 4 = 4, 8, 12, 16, 20, ….
Multiples of 6 = 6, 12, 18, 24, 30, …..
Therefore, the LCM of 2, 4 and 6 is 12.
Frequently Asked Questions on LCM of 2, 4 and 6
Determine the GCF if the LCM of 2, 4 and 6 is 12.
We know that
LCM x GCF = 2 x 4 x 6
As LCM (2, 4, 6) is 12
12 x GCF = 48
GCF = 48/12 = 4
What is the LCM of 2, 4 and 6?
The LCM of 2, 4 and 6 is 12. First we have to find the multiples of 2, 4 and 6 to find the LCM
Multiples of 2 = 2, 4, 6, 8, 10, ……
Multiples of 4 = 4, 8, 12, 16, 20, ….
Multiples of 6 = 6, 12, 18, 24, 30, ….
The smallest multiple exactly divisible by 2, 4 and 6 is 12.
Write the relation between GCF and LCM of 2, 4 and 6.
The relation between GCF and LCM of 2, 4 and 6 is
LCM x GCF = 2 x 4 x 6
LCM x GCF = 48
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