LCM of 12 and 42 is 84. LCM is used to optimize the given set of quantities in real world situations. 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 12 and 42, 84 is the first(least or smallest) number that is common for the multiples of 12 and 42. The LCM is also known as LCD, Least Common Divisor for 12 and 42 is 84. You can refer to HCF and LCM to differentiate between LCM and HCF.
What is LCM of 12 and 42
The Least Common Multiple or Lowest Common Multiple of 12 and 42 is 84.
How to Find LCM of 12 and 42?
LCM of 12 and 42 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 42 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 12 and 42 can be expressed as;
12 = 2 x 2 x 3
42 = 2 x 3 x 7
LCM (12, 42) = 2 x 2 x 3 x 7 = 84
LCM of 12 and 42 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 |
12 |
42 |
|
3 |
6 |
21 |
|
2 |
2 |
7 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
Hence, LCM (12, 42) = 2 x 2 x 3 x 7 = 84
LCM of 12 and 42 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 12 and 42.
|
Multiples of 12 |
Multiples of 42 |
|
12 |
42 |
|
24 |
84 |
|
36 |
126 |
|
48 |
168 |
|
84 |
210 |
|
72 |
252 |
|
84 |
294 |
LCM (12, 42) = 84
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 12 and 42?
Answer: 84 is the smallest number that is divisible by both 12 and 42.
What is the LCM for 2, 12 and 42?
Answer: LCM for 2, 12 and 42 is 84.
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