LCM of 54 and 60 is 540. The Least Common Divisor (LCD) also known as Least Common Multiple or Lowest common multiple(LCM) is the smallest numeral that is divisible by the given group of numbers. In the given set of numbers 54 and 60, 540 is the first(least or smallest) number that is common in the set of multiples of 54 and 60. You can use LCM Formula to find the LCM of 2 numbers.
What is LCM of 54 and 60
The Least Common Multiple or Lowest Common Multiple of 54 and 60 is 540.
How to Find LCM of 54 and 60?
LCM of 54 and 60 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 54 and 60 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 54 and 60 can be expressed as;
54 = 2 × 3 × 3 × 3
60 = 2 × 2 × 3 × 5
2 × 3 are the common factors for 54 and 60, which is multiplied by the other factors of 54 and 60 to get the LCM.
LCM (54, 60) = 2 × 2 × 3 × 3 × 3 × 5 = 540
LCM of 54 and 60 Using Division Method
In the Division Method, the numbers 54 and 60 are divided together by prime divisors starting from the smallest and increasing it by the divisibility. The product of the prime divisors forms the LCM.
|
2 |
54 |
60 |
|
2 |
27 |
30 |
|
3 |
27 |
15 |
|
3 |
9 |
5 |
|
3 |
3 |
5 |
|
5 |
1 |
5 |
|
× |
1 |
1 |
LCM (54, 60) = 2 × 2 × 3 × 3 × 3 × 5 = 540
LCM of 54 and 60 Using Listing the Multiples
By listing all the multiples of 54 and 60, we can identify the least common multiple, which is the LCM. Below is the list of multiples for 54 and 60
|
Multiples of 54 |
Multiples of 60 |
|
54 |
60 |
|
108 |
120 |
|
162 |
180 |
|
216 |
240 |
|
270 |
300 |
|
324 |
360 |
|
378 |
420 |
|
432 |
480 |
|
486 |
540 |
|
540 |
600 |
LCM (54, 60) = 540
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 54 and 60?
Answer: 540 is the smallest number that is divisible by both 54 and 60.
What is the LCM for 5, 54 and 60?
Answer: LCM for 5, 54 and 60 is 540 as 5 is the prime factor of 60.
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