LCM of 12, 24 and 36 is 72. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.Among all common multiples of 12, 24, and 36, the LCM of 12, 24, and 36 is the smallest number. (12, 24, 36, 48, 60… ), (24, 48, 72, 96, 120… ), and (36, 72, 108, 144, 180… ), respectively, are the first few multiples of 12, 24, and 36. Prime factorization, division, and listing multiples are the three most frequent methods for calculating the LCM of 12, 24, and 36..
Also read: Least common multiple
What is LCM of 12, 24 and 36?
The answer to this question is 72. The LCM of 12, 24 and 36 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 36, is the smallest positive integer 72 which is divisible by both 24 and 36 with no remainder.
How to Find LCM of 12, 24 and 36?
LCM of 12, 24 and 36 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12, 24 and 36 Using Prime Factorisation Method
The prime factorisation of 24 and 36, respectively, is given by:
12 = (2 × 2 × 3) = 22 × 31
24 = 2 x 2 x 2 x 3 = 2³x 31
36 = 2 x 2 x 3 x 3 = 2² x 3²
LCM (12, 24, 36) = 72
LCM of 12, 24 and 36 Using Division Method
We’ll divide the numbers (12, 24, 36) by their prime factors to get the LCM of 12, 24 and 36 using the division method (preferably common). The LCM of 12, 24 and 36 is calculated by multiplying these divisors.
| 2 | 12 | 24 | 36 |
| 2 | 6 | 12 | 18 |
| 2 | 3 | 6 | 9 |
| 2 | 3 | 3 | 9 |
| 3 | 3 | 1 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (12, 24, 36) = 72
LCM of 12, 24 and 36 Using Listing the Multiples
To calculate the LCM of 12, 24 and 36 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 24 | Multiples of 36 |
| 12 | 24 | 36 |
| 24 | 48 | 72 |
| 36 | 72 | 108 |
| 48 | 96 | 144 |
| 60 | 120 | 180 |
| 72 | 144 | 216 |
The smallest common multiple of 24 and 36 is 72.
Therefore LCM (12, 24, 36) = 72
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LCM of 12, 24 and 36 Solved Example
Find the smallest number that is divisible by 12, 24, 36 exactly.
Solution:
The smallest number that is divisible by 12, 24, and 36 exactly is their LCM.
⇒ Multiples of 12, 24, and 36:
Multiples of 12 = 12, 24, 36, 48, 60, 72, . . . .
Multiples of 24 = 24, 48, 72, 96, 120, 144, . . . .
Multiples of 36 = 36, 72, 108, 144, 180, 216, . . . .
Therefore, the LCM of 12, 24, and 36 is 72.
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