LCM of 378 180 and 420

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.

lcm of 378 180 and 420

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.

Frequently Asked Questions on LCM of 378, 180 and 420

Q1

What is the LCM of 378, 180 and 420?

The LCM of 378, 180 and 420 is 3780.
Q2

Is the LCM of 378, 180 and 420 the same as the HCF of 378, 180 and 420?

No. LCM of 378, 180 and 420 is 3780 and HCF of 378, 180 and 420 is 6.
Q3

What are the common prime factors of 378, 180 and 420?

The common prime factors of 378, 180 and 420 are 2 and 3.
Q4

What are the first 3 common multiples of 378, 180 and 420?

The first three common multiples of 378, 180 and 420 are 3780, 7560, and 11340.
Q5

Is the LCM of 378 and 180 the same as the LCM of 378 and 420?

Yes. LCM of 378 and 180 is 3780, whereas the LCM of 378 and 420 is 3780. They are the same.

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*