LCM of 72 and 108 is 216. Among all common multiples of 72 and 108, the LCM of 72 and 108 is the smallest. (72, 144, 216, 288, etc.) and (108, 216, 324, 432, 540, etc.) are the first few multiples of 72 and 108. Prime factorization, listing multiples, and division are the three most frequent methods for determining the LCM of 72 and 108. In mathematics, the LCM of any two numbers is the value that divides the two values equally.
What is LCM of 72 and 108?
The answer to this question is 216. The LCM of 72 and 108 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 72 and 108, is the smallest positive integer 216 which is divisible by both 72 and 108 with no remainder.
Also read: Least common multiple
How to Find LCM of 72 and 108?
LCM of 72 and 108 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 72 and 108 Using Prime Factorisation Method
The prime factorisation of 72 and 108, respectively, is given by:
72 = (2 × 2 × 2 × 3 × 3) = 23 × 32 and
108 = (2 × 2 × 3 × 3 × 3) = 22 × 33
LCM (72, 108) = 216
LCM of 72 and 108 Using Division Method
We’ll divide the numbers (72, 108) by their prime factors to get the LCM of 72 and 108 using the division method (preferably common). The LCM of 72 and 108 is calculated by multiplying these divisors.
| 2 | 72 | 108 |
| 2 | 36 | 54 |
| 3 | 18 | 27 |
| 3 | 6 | 9 |
| 3 | 2 | 3 |
| 2 | 2 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (72, 108) = 216
LCM of 72 and 108 Using Listing the Multiples
To calculate the LCM of 72 and 108 by listing out the common multiples, list the multiples as shown below:
| Multiples of 72 | Multiples of 108 |
| 72 | 108 |
| 144 | 216 |
| 216 | 324 |
| 288 | 432 |
| 360 | 540 |
The smallest common multiple of 72 and 108 is 216.
LCM (72, 108) = 216
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LCM of 72 and 108 Solved Example
The GCD and LCM of two numbers are 36 and 216 respectively. If one number is 108, find the other number.
Let the other number be b.
GCD × LCM = 108 × b
b = (GCD × LCM)/108
b = (36 × 216)/108
b = 72
Therefore, the other number is 72.
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