LCM of 24, 36 and 40 is 360. Students who want to obtain proficiency in finding the LCM and HCF of given numbers can rely on the article HCF and LCM. This article is designed by experts with the purpose of providing the best study source for students. Solving the problems following this article helps students to clarify their doubts immediately and enhances skills that are vital to score good marks in exams. Let us grasp the simple method on how to find the least common multiple of 24, 36 and 40 in this article.
What is LCM of 24, 36 and 40?
The answer to this question is 360.
How to Find LCM of 24, 36 and 40?
The LCM of 24, 36 and 40 can be determined by using the methods mentioned below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24, 36 and 40 Using Prime Factorisation Method
By prime factorisation method, we can write 24, 36 and 40 as the product of prime numbers, such that;
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
40 = 2 × 2 × 2 × 5
LCM (24, 36, 40) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 24, 36 and 40 Using Division Method
In the division method, we divide the numbers 24, 36 and 40 by their prime factors until we get the result as one in the complete row to determine their LCM. The product of these divisors gives the least common multiple of 24, 36 and 40.
| 2 | 24 | 36 | 40 |
| 2 | 12 | 18 | 20 |
| 2 | 6 | 9 | 10 |
| 3 | 3 | 9 | 5 |
| 3 | 1 | 3 | 5 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No more further division can be done.
Hence, LCM (24, 36, 40) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 24, 36, and 40 Using Listing the Multiples
Here, we list out the multiples of 24, 36 and 40 to calculate the least common multiple of 24, 36 and 40 in a precise manner. The multiples of 24, 36 and 40 are as follows:
Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, ………., 312, 336, 360, …………
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, ………
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, …………
LCM (24, 36, 40) = 360
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Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by 24, 36, 40 exactly?
Solution: 360 is the smallest number that is divisible by 24, 36, 40 exactly.
Q. 2: Find the LCM of 24, 36 and 40 using the division method.
Solution: We can determine the least common multiple of 24, 36 and 40 using the division method as below.
| 2 | 24 | 36 | 40 |
| 2 | 12 | 18 | 20 |
| 2 | 6 | 9 | 10 |
| 3 | 3 | 9 | 5 |
| 3 | 1 | 3 | 5 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
Thus the LCM (24, 36, 40) = 2 × 2 × 2 × 3 × 3 × 5 = 360
Frequently Asked Questions on LCM of 24, 36 and 40
Write is the LCM of 24, 36 and 40.
Is the LCM of 24, 36 and 40 the same as the HCF of 24, 36 and 40?
360 is the LCM of 24, 36 and 40. True or False.
What are the methods used to find the LCM of 24, 36 and 40?
The following methods are used to find the LCM of 24, 36 and 40
Prime Factorisation
Division Method
Listing the Multiples
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