LCM of 10 and 12 is 60. The Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 10 and 12, 60 is the first (least or smallest) number that is common in the set of multiples of 10 and 12. The LCM is also known as LCD, Least Common Divisor for 10 and 12 is 60. You can refer to the LCM with Examples.
What is LCM of 10 and 12
The Least Common Multiple or Lowest Common Multiple of 10 and 12 is 60.
How to Find LCM of 10 and 12?
LCM of 10 and 12 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 12 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 10 and 12 can be expressed as;
10 = 2 x 5
12 = 2 x 2 x 3
LCM (10, 12) = 2 x 2 x 3 x 5 = 60
LCM of 10 and 12 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
|
2 |
10 |
12 |
|
2 |
5 |
6 |
|
3 |
5 |
3 |
|
5 |
5 |
1 |
|
x |
1 |
1 |
Hence, LCM (10, 12) = 2 x 2 x 3 x 5 = 60
LCM of 10 and 12 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 10 and 12
|
Multiples of 10 |
Multiples of 12 |
|
10 |
12 |
|
20 |
24 |
|
30 |
36 |
|
40 |
48 |
|
50 |
60 |
|
60 |
72 |
|
70 |
105 |
LCM (10, 12) = 60
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 10 and 12?
Answer: 60 is the smallest number that is divisible by both 10 and 12.
What is the LCM for 1, 10 and 12?
Answer: LCM for 1, 10 and 12 is 60.
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