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LCM of 2, 4 and 6

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

Related Articles

Video Lesson on Applications of LCM

LCM of 2, 4 and 6 Solved Examples 

Question: What is the smallest number divisible by 2, 4 and 6 exactly?

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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