LCM of 3, 9 and 12 is 36. LCM stands for Least Common Multiple or the Lowest Common Multiple also known as LCD Least Common Divisor is the positive number that is a common multiple to the given numbers. Here the given set of numbers are 3, 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 with Examples to understand better.
What is LCM of 3, 9 and 12
The Least Common Multiple or Lowest Common Multiple of 3, 9 and 12 is 36.
How to Find LCM of 3, 9 and 12?
LCM of 3, 9 and 12 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 9 and 12 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 3, 9 and 12 can be expressed as;
3 = 1 × 3
9 = 3 × 3
12 = 2 × 2 × 3
3 is the common factor of 3, 9 and 12. 3 along with other prime factors of 9 and 12 are multiplied to get the LCM.
LCM(3, 9 and 12) = 2 × 2 × 3 × 3 = 36
LCM of 3, 9 and 12 Using Division Method
In the Division Method, the numbers 3, 9 and 12 are divided by common prime divisors. The product of common and other prime divisors of 3, 9 and 12 forms the LCM.
|
2 |
3 |
9 |
12 |
|
2 |
3 |
9 |
6 |
|
3 |
3 |
9 |
3 |
|
3 |
1 |
3 |
1 |
|
× |
1 |
1 |
1 |
LCM(3, 9 and 12) = 2 × 2 × 3 × 3 = 36
LCM of 3, 9 and 12 Using Listing the Multiples
By listing all the multiples of 3, 9 and 12, we can identify the LCM. Below is the list of multiples for 3, 9 and 12
|
Multiples of 3 |
Multiples of 9 |
Multiples of 12 |
|
3 |
9 |
12 |
|
6 |
18 |
24 |
|
9 |
27 |
36 |
|
12 |
36 |
48 |
|
15 |
45 |
60 |
|
18 |
54 |
72 |
|
21 |
63 |
84 |
|
24 |
72 |
96 |
|
27 |
81 |
108 |
|
30 |
90 |
120 |
|
33 |
99 |
132 |
|
36 |
108 |
144 |
LCM(3, 9 and 12) = 36
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 3, 9 and 12?
Answer: 36 is the smallest number that is divisible by 3, 9 and 12.
What is the LCM of 3 and 36?
Answer: LCM of 3 and 36 is 36.
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