LCM of 36, 54 and 72 is 216. LCM is also known as Least Common Multiple or Lowest common multiple. LCM is the smallest multiple that is common to a given group of numbers. It is also the smallest number that is divisible by the same set of given numbers. Consider the example for finding the LCM of 36, 54 and 72. The answer is 216. 216 is divisible by 36, 54 and 72. Even 432 is divisible by 36, 54 and 72, however it is not the LCM for 36, 54 and 72. The smaller number than 432 is 216 which is divisible by 36, 54 and 72. Hence 216 is the Least Common Multiple for 36, 54 and 72. You can refer to LCM for more details.
What is LCM of 36, 54 and 72
The Least Common Multiple or Lowest Common Multiple of 36, 54 and 72 is 216.
How to Find LCM of 36, 54 and 72?
LCM of 36, 54 and 72 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36, 54 and 72 Using Prime Factorisation Method
In the Prime Factorisation method, 36, 54 and 72 can be expressed as;
36 = 2 × 2 × 3 × 3
54 = 2 × 3 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
The factors that satisfy all the three numbers are considered as the LCM.
Therefore, LCM (36, 54 and 72) = 2 × 2 × 2 × 3 × 3 × 3 = 216
LCM of 36, 54 and 72 Using Division Method
For the Division Method, the numbers 36, 54 and 72 are divided till the remainders are 1 and dividing them with only prime divisors in increasing order of divisibility. The product of those prime divisors will be the LCM.
|
2 |
36 |
54 |
72 |
|
2 |
18 |
27 |
36 |
|
2 |
9 |
27 |
18 |
|
3 |
9 |
27 |
9 |
|
3 |
3 |
9 |
3 |
|
3 |
1 |
3 |
1 |
|
× |
1 |
1 |
1 |
LCM (36, 54 and 72) = 2 × 2 × 2 × 3 × 3 × 3 = 216
LCM of 36, 54 and 72 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the least common multiple, which is the LCM. Below is the list of multiples for 36, 54 and 72.
|
Multiples of 36 |
Multiples of 54 |
Multiples of 72 |
|
36 |
54 |
72 |
|
72 |
108 |
144 |
|
108 |
162 |
216 |
|
144 |
216 |
288 |
|
180 |
270 |
360 |
|
216 |
360 |
432 |
LCM (36, 54 and 72) = 216
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 36, 54 and 72?
Answer: 216 is the smallest number that is divisible by 36, 54 and 72.
What is the LCM for 2 and 216?
Answer: LCM for 2 and 216 is 216 as 2 is the factor of 216.
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