LCM of 24, 36 and 48 is 144. The smallest number among all common multiples of 24, 36, and 48 is the LCM of 24, 36, and 48. (24, 48, 72, 96, 120…), (36, 72, 108, 144, 180…), and (48, 96, 144, 192, 240…), respectively, are the first few multiples of 24, 36, and 48. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 24, 36 and 48?
The answer to this question is 144. The LCM of 24, 36 and 48 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24, 36 and 48, is the smallest positive integer 144 which is divisible by both 24, 36 and 48 with no remainder.
How to Find LCM of 24, 36 and 48?
LCM of 24, 36 and 48 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24, 36 and 48 Using Prime Factorisation Method
The prime factorisation of 24, 36 and 48, respectively, is given by:
24 = 2 x 2 x 2 x 3 = 2³x 3
36 = 2 x 2 x 3 x 3 = 2² x 3²
48 = (2 × 2 × 2 × 2 × 3) = 24 × 31
LCM (24, 36, 48) = 144
LCM of 24, 36 and 48 Using Division Method
We’ll divide the numbers (24, 36, 48) by their prime factors to get the LCM of 24, 36 and 48 using the division method (preferably common). The LCM of 24, 36 and 48 is calculated by multiplying these divisors.
| 2 | 24 | 36 | 48 |
| 2 | 12 | 18 | 24 |
| 2 | 6 | 9 | 12 |
| 2 | 3 | 9 | 6 |
| 3 | 1 | 3 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (24, 36, 48) = 144
LCM of 24, 36 and 48 Using Listing the Multiples
To calculate the LCM of 24, 36 and 48 by listing out the common multiples, list the multiples as shown below.
| Multiples of 24 | Multiples of 36 | Multiples of 48 |
| 24 | 36 | 48 |
| 48 | 72 | 96 |
| 72 | 108 | 144 |
| 96 | 144 | 192 |
| 120 | 180 | 240 |
| 144 | 216 | 288 |
The smallest common multiple of 24, 36 and 48 is 144.
Therefore LCM (24, 36, 48) = 144
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LCM of 24, 36 and 48 Solved Example
Question: Calculate the LCM of 24, 36, and 48 using the GCD of the given numbers.
Solution:
Prime factorization of 24, 36, 48:
24 = 2³x 3
36 = 2² x 3²
48 = 24 × 31
Therefore, GCD(24, 36) = 12, GCD(36, 48) = 12, GCD(24, 48) = 24, GCD(24, 36, 48) = 12
We know,
LCM(24, 36, 48) = [(24 × 36 × 48) × GCD(24, 36, 48)]/[GCD(24, 36) × GCD(36, 48) × GCD(24, 48)]
LCM(24, 36, 48) = (41472 × 12)/(12 × 12 × 24) = 144
Therefore LCM(24, 36, 48) = 144
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