LCM of 60, 84 and 108 is 3780. LCM also known as Least Common multiple or Lowest common multiple 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 60, 84 and 108. The answer is 3780. 3780 is divisible by 60, 84 and 108. Hence 3780 is the Least Common Multiple for 60, 84 and 108. You can refer to LCM for more information.
What is LCM of 60, 84 and 108
The Least Common Multiple or Lowest Common Multiple of 60, 84 and 108 is 3780.
How to Find LCM of 60, 84 and 108?
LCM of 60, 84 and 108 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60, 84 and 108 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 60, 84 and 108 can be expressed as;
60 = 2 x 2 x 3 x 5
84 = 2 x 2 x 3 x 7
108 = 2 x 2 x 3 x 3 x 3
LCM (60, 84, 108) = 2 x 2 x 3 x 3 x 3 x 5 x 7 = 3780
LCM of 60, 84 and 108 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 |
60 |
84 |
108 |
|
2 |
30 |
42 |
54 |
|
3 |
15 |
21 |
27 |
|
3 |
5 |
7 |
9 |
|
3 |
5 |
7 |
3 |
|
5 |
5 |
7 |
1 |
|
7 |
1 |
7 |
1 |
|
x |
1 |
1 |
1 |
LCM (60, 84, 108) = 2 x 2 x 3 x 3 x 3 x 5 x 7 = 3780
LCM of 60, 84 and 108 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 60, 84 and 108
- Multiples of 60: 60, 120, 180, 240, 300, 360,, ….… 3660, 3720, 3780, 3840 …
- Multiples of 84: 84, 168, 252, …., 3612, 3696, 3780, 3864, …
- Multiples of 108: 108, 216, 324, 432….3564, 3672, 3780, 3888,
LCM (60, 84, 108) = 3780
Related Articles
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by 60, 84 and 108?
Answer: 3780 is the smallest number that is divisible by 60, 84 and 108.
2. What is the LCM of 60 and 84?
Answer: LCM of 60 and 84 is 420.
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