LCM of 6, 9 and 12 is 36. LCM/LCD stands for Least/Lowest Common Multiple and Least Common Divisor is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 6, 9 and 12. The smallest common multiple for all these numbers among many is 36, and hence it is the LCM. You can refer to LCM for all details.
What is LCM of 6, 9 and 12
The Least Common Multiple or Lowest Common Multiple of 6, 9 and 12 is 36.
How to Find LCM of 6, 9 and 12?
LCM of 6, 9 and 12 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 9 and 12 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 6, 9 and 12 can be expressed as;
6 = 2 × 3
9 = 3 × 3
12 = 2 × 2 × 3
Here 3 is the common factor of 6, 9 and 12 along with other factors which are multiplied to get the LCM.
LCM (6, 9 and 12) = 2 × 2 × 3 × 3 = 36
LCM of 6, 9 and 12 Using Division Method
In the Division Method, dividing 6, 9 and 12 with prime divisors, till the reminders are 1 when divided together. The product of the prime divisors forms the LCM.
|
2 |
6 |
9 |
12 |
|
2 |
3 |
9 |
6 |
|
3 |
3 |
9 |
3 |
|
3 |
1 |
3 |
1 |
|
× |
1 |
1 |
1 |
LCM(6, 9 and 12) = 2 × 2 × 3 × 3 = 36
LCM of 6, 9 and 12 Using Listing the Multiples
By listing all the multiples of 6, 9 and 12, we can identify the LCM. Below is the list of multiples for 6, 9 and 12
|
Multiples of 6 |
Multiples of 9 |
Multiples of 12 |
|
6 |
9 |
12 |
|
12 |
18 |
24 |
|
18 |
27 |
36 |
|
24 |
36 |
48 |
|
30 |
45 |
60 |
|
36 |
54 |
72 |
LCM (6, 9 and 12) = 36
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 6, 9 and 12?
Answer: 36 is the smallest number that is divisible by 6, 9 and 12.
What is the LCM of 2, 3, 6, 9 and 12?
Answer: LCM of 2, 3, 6, 9 and 12 is 36 as 2 is the factor for 6 and 12 whereas 3 is the factor for 6, 9 and 12.
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