LCM of 24, 30 and 40 is 120. 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. LCM of 24, 30, and 40 is the smallest number among all common multiples of 24, 30, and 40. The first few multiples of 24, 30, and 40 are (24, 48, 72, 96, 120 . . .), (30, 60, 90, 120, 150 . . .), and (40, 80, 120, 160, 200 . . .) respectively.
Also read: Least common multiple
What is LCM of 24, 30 and 40?
The answer to this question is 120. The LCM of 24, 30 and 40 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24, 30 and 40, is the smallest positive integer 120 which is divisible by both 24, 30 and 40 with no remainder.
How to Find LCM of 24, 30 and 40?
LCM of 24, 30 and 40 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24, 30 and 40 Using Prime Factorisation Method
The prime factorisation of 24, 30 and 40, respectively, is given by:
24 = (2 × 2 × 2 × 3) = 23 × 31,
30 = (2 × 3 × 5) = 21 × 31 × 51, and
40 = (2 × 2 × 2 × 5) = 23 × 51
LCM (24, 30, 40) = 120
LCM of 24, 30 and 40 Using Division Method
We’ll divide the numbers (24, 30, 40) by their prime factors to get the LCM of 24, 30 and 40 using the division method (preferably common). The LCM of 24, 30 and 40 is calculated by multiplying these divisors.
| 2 | 24 | 30 | 40 |
| 2 | 12 | 15 | 20 |
| 2 | 6 | 15 | 10 |
| 3 | 3 | 15 | 5 |
| 5 | 1 | 5 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (24, 30, 40) = 120
LCM of 24, 30 and 40 Using Listing the Multiples
To calculate the LCM of 24, 30 and 40 by listing out the common multiples, list the multiples as shown below
| Multiples of 24 | Multiples of 30 | Multiples of 40 |
| 24 | 30 | 40 |
| 48 | 60 | 80 |
| 72 | 90 | 120 |
| 96 | 120 | 160 |
| 120 | 150 | 200 |
The smallest common multiple of 24, 30 and 40 is 120.
Therefore LCM (24, 30, 40) = 120
Related Articles
Video Lesson on Applications of LCM
LCM of 24, 30 and 40 Solved Example
Calculate the LCM of 24, 30, and 40 using the GCD of the given numbers.
Solution:
Prime factorization of 24, 30, 40:
24 = 23 × 31
30 = 2 × 3 × 5
40 = 23 × 51
Therefore, GCD(24, 30) = 6, GCD(30, 40) = 10, GCD(24, 40) = 8, GCD(24, 30, 40) = 2
We know,
LCM(24, 30, 40) = [(24 × 30 × 40) × GCD(24, 30, 40)]/[GCD(24, 30) × GCD(30, 40) × GCD(24, 40)]
LCM(24, 30, 40) = (28800 × 2)/(6 × 10 × 8) = 120
⇒LCM(24, 30, 40) = 120
Frequently Asked Questions on LCM of 24, 30 and 40
What is the LCM of 24, 30 and 40?
List the methods used to find the LCM of 24, 30 and 40.
What is the Least Perfect Square Divisible by 24, 30, and 40?
LCM of 24, 30, and 40 = 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5] ⇒ Least perfect square divisible by each 24, 30, and 40 = LCM(24, 30, 40) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
Comments