LCM of 378, 180 and 420 is 3780. 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 378, 180 and 420, 3780 is the first(least or smallest) number that is common in the set of multiples of 378, 180 and 420. The LCM, also known as LCD, Least Common Divisor for 378, 180 and 420 is 3780. You can use the LCM for more clarity. LCM is used in fraction problems.
What is LCM of 378, 180 and 420
The Least Common Multiple or Lowest Common Multiple of 378, 180 and 420 is 3780.
How to Find LCM of 378, 180 and 420?
LCM of 378, 180 and 420 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 378, 180 and 420 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 378, 180 and 420 can be expressed as;
378 = 2 × 3 × 3 × 3 × 7
180 = 2 × 2 × 3 × 3 × 5
420 =2 × 2 × 3 × 5 × 7
LCM (378, 180, 420) = 2 × 2 × 3 × 3 × 3 × 5 × 7 = 3780
LCM of 378, 180 and 420 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 |
378 |
180 |
420 |
|
2 |
189 |
90 |
210 |
|
3 |
189 |
45 |
105 |
|
3 |
63 |
15 |
35 |
|
5 |
21 |
5 |
35 |
|
7 |
21 |
1 |
7 |
|
3 |
3 |
1 |
1 |
|
× |
1 |
1 |
1 |
No further division is possible as only prime numbers are left. Hence
LCM (378, 180, 420) = 2 × 2 × 3 × 3 × 3 × 5 × 7 = 3780
LCM of 378, 180 and 420 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 378, 180 and 420
Multiples of 378:
378, 756, 1134, 1512, 1890, 2268, 2646, 3024, 3402, 3780, 4158, 4536, 4914 …
Multiples of 180:
180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320 …
Multiples of 420:
420, 840, 1260, 1680, 2100, 2520, 2940, 3360, 3780, 4200, 4620, 5040 …
LCM (378, 180, 420) = 3780
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 378, 180 and 420?
Answer: 3780 is the smallest number that is divisible by 378, 180 and 420.
What is the LCM for 2, 3, 7, 378, 180 and 420?
Answer: LCM for 2, 3, 7, 378, 180 and 420 is 3780.
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