LCM of 24, 15 and 36 is 360. The lowest common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. Least Common Multiple (LCM) is a vital study material for students to rely on for effective exam preparation. The highly skilled subject experts curated this article to help students grasp the LCM concept more effectively. Let us learn the simple format of finding the least common multiple of 24, 15 and 36 with solved examples and FAQs here.
What is LCM of 24, 15 and 36?
The Least Common Multiple of 12, 15 and 36 is 360.
How to Find LCM of 24, 15 and 36?
The LCM of 24, 15 and 36 can be determined by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 24, 15 and 36 Using Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Hence the numbers 24, 15 and 36 can be expressed as;
24 = 2 × 2 × 2 × 3
15 = 3 × 5
36 = 2 × 2 × 3 × 3
LCM (24, 15, 36) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 24, 15 and 36 Using Division Method
In the division method, to calculate the LCM, we divide the numbers 24, 15 and 36 by their prime factors until we get the result as one in the complete row. The product of these divisors represents the least common multiple of 24, 15 and 36.
| 2 | 24 | 15 | 36 |
| 2 | 12 | 15 | 18 |
| 2 | 6 | 15 | 9 |
| 3 | 3 | 15 | 9 |
| 3 | 1 | 5 | 3 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (24, 15, 36) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 24, 15 and 36 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the least common multiple among them. The below list shows the multiples of 24, 15 and 36.
Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, ……………, 312, 336, 360, ……
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ………, 330, 345, 360, …….
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, ………..
LCM (24, 15, 36) = 360
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by 24,15,36 exactly?
Solution: The smallest number that is divisible by 24, 15, 36 exactly is their LCM. 360 is the LCM of 24, 15 and 36. Therefore the smallest number that is divisible by 24, 15, 36 exactly is 360.
Frequently Asked Questions on LCM of 24, 15 and 36
What is the LCM of 24, 15 and 36?
What is the LCM of 24, 15 and 36 and the HCF of 24, 15 and 36?
Mention the methods used to find the LCM of 24, 15 and 36.
The following methods are used to find the LCM of 24, 15 and 36
Prime Factorisation
Division Method
Listing the Multiples
Find the LCM of 24, 15 and 36 using the prime factorisation method.
Here, we express the given numbers as the product of prime factors
24 = 2 × 2 × 2 × 3
15 = 3 × 5
36 = 2 × 2 × 3 × 3
LCM (24, 15, 36) = 2 × 2 × 2 × 3 × 3 × 5 = 360
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