LCM of 84, 90 and 120 is 2520. LCM stands for Least Common Multiple or the Lowest common multiple also known as LCD Least Common Divisor is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 84, 90 and 120. The smallest common multiple for all these numbers among many is 2520, and hence it is the LCM. You can refer to the LCM with Examples.
What is LCM of 84, 90 and 120
The Least Common Multiple or Lowest Common Multiple of 84, 90 and 120 is 2520.
How to Find LCM of 84, 90 and 120?
LCM of 84, 90 and 120 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 84, 90 and 120 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 84, 90 and 120 can be expressed as;
84 = 2 x 2 x 3 x 7
90 = 2 x 3 x 3 x 5
120 = 2 x 2 x 2 x 3 x 5
LCM (84, 90 and 120) = 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520
LCM of 84, 90 and 120 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 |
84 |
90 |
120 |
|
3 |
42 |
45 |
60 |
|
2 |
14 |
15 |
20 |
|
5 |
7 |
15 |
10 |
|
2 |
7 |
3 |
2 |
|
3 |
7 |
3 |
1 |
|
7 |
7 |
1 |
1 |
|
x |
1 |
1 |
1 |
LCM (84, 90 and 120) = 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520
LCM of 84, 90 and 120 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 84, 90 and 120
Multiples of 84:
84, 168, 252, …, 672, 756, 840, 924, 1008, …, 1344, 1428, 1512, 1596, …. 1932, 2016, 2100, .., 2436, 2520, 2604, …
Multiples of 90:
90, 180, 270, … 720, 810, 900, 990, …1350, 1440, 1530, .. 1890, 1980, 2070,…2430, 2520, 2610, …
Multiples of 120:
120, 240, 360, …, 1080, 1200, 1320, …, 1920, 2040, .., 2400, 2520, 2640, …..
LCM (84, 90 and 120) = 2520
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 84, 90 and 120?
Answer: 2520 is the smallest number that is divisible by 84, 90 and 120.
What is the LCM of 90 and 120?
Answer: LCM of 90 and 120 is 360.
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