LCM of 12, 30 and 42 is 420. LCM is an abbreviation for Least Common Multiple/Lowest common multiple. It is the smallest or the least positive integer that is divisible by the given set of numbers. Consider the example for finding the LCM of 12, 30 and 42. The answer is 420. 420 is divisible by 12, 30 and 42. Even 840 is divisible by 12, 30 and 42, however it is not the LCM for 12, 30 and 42. The smaller number than 840 is 420 which is divisible by 12, 30 and 42. Hence 420 is the Least Common Multiple for 12, 30 and 42. You can refer to LCM for more details.
What is LCM of 12, 30 and 42
The Least Common Multiple or Lowest Common Multiple of 12, 30 and 42 is 420.
How to Find LCM of 12, 30 and 42?
LCM of 12, 30 and 42 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 30 and 42 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 12, 30 and 42 can be expressed as the product of prime numbers. Here, 12, 30 and 42 can be expressed as;
12 = 2 × 2 × 3
30 = 2 × 3 × 5
42 = 2 × 3 × 7
The common product of these prime factors forms the LCM.
LCM (12, 30 and 42) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 12, 30 and 42 Using Division Method
In the Division Method, divide all the numbers with prime factors, starting from the smallest. The product of the prime factors is the LCM.
The division is shown in the table below;
|
2 |
12 |
30 |
42 |
|
3 |
6 |
15 |
21 |
|
2 |
2 |
5 |
7 |
|
5 |
1 |
5 |
7 |
|
7 |
1 |
1 |
7 |
|
× |
1 |
1 |
1 |
LCM (12, 30 and 42) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 12, 30 and 42 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first common multiple, which is the LCM. Below is the list of multiples for 12, 30 and 42
Multiples of 12
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444
Multiples of 30
30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480
Multiples of 42
42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504
LCM (12, 30 and 42) = 420
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 12, 30 and 42?
Answer: 420 is the smallest number that is divisible by 12, 30 and 42.
What is the LCM for 42 and 420?
Answer: LCM for 42 and 420 is 420.
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