LCM of 18, 24 and 36 is 72. LCM denotes the smallest positive number that is a multiple of two or more numbers. Solving the textbook problem with the help of the article Least Common Multiple (LCM) will build skills and techniques among students, which is significant from the exam perspective. Highly knowledgeable faculty members designed this article to enable students to score good marks in exams. In this article, let us grasp the technique of determining the least common multiple of 18, 24 and 36 in a simple format.
What is LCM of 18, 24 and 36?
The answer to this question is 72.
How to Find LCM of 18, 24 and 36?
We can determine the LCM of 18, 24 and 36 by using the methods given below:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 18 24 and 36 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 18 24 and 36 can be expressed as;
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
LCM (18, 24, 36) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 18 24 and 36 Using Division Method
In this method, we divide the numbers 18, 24 and 36 by a common prime number until the remainder is a prime number or one. The product of these divisors denotes the least common multiple of 18, 24 and 36.
| 2 | 18 | 24 | 36 |
| 2 | 9 | 12 | 18 |
| 2 | 9 | 6 | 9 |
| 3 | 9 | 3 | 9 |
| 3 | 3 | 1 | 3 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (18, 24, 36) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 18, 24 and 36 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to find the lowest common multiple among them. Let us glance at the multiples of 18, 24 and 36 from the table given below.
| Multiples of 18 | Multiples of 24 | Multiples of 36 |
| 18 | 24 | 36 |
| 36 | 48 | 72 |
| 54 | 72 | 108 |
| 72 | 96 | 144 |
| 90 | 120 | 180 |
LCM (18, 24, 36) = 72
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by 18, 24, 36 exactly?
Solution: The smallest number that is divisible by 18, 24 and 36 is their LCM. Below is the list of multiples for 18, 24 and 36.
Multiples of 18 : 18, 36, 54, 72, 90, 108, 126, ………
Multiples of 24 : 24, 48, 72, 96, 120, 144, 168, ………
Multiples of 36 : 36, 72, 108, 144, 180, 216, 252, ……….
Therefore 72 is the smallest number that is divisible by 18, 24,36 exactly.
2. What is the lowest common factor of 18, 24 and 36?
Solution: The lowest common factor of 18, 24 and 36 is 72.
Frequently Asked Questions on LCM of 18, 24 and 36
What is the LCM of 18, 24 and 36?
Is the LCM of 18, 24 and 36 the same as the HCF of 18, 24 and 36?
Is 92 the LCM of 18, 24 and 36?
Mention the methods used to determine the LCM of 18, 24 and 36.
The following methods are used to determine the LCM of 18, 24 and 36
Prime Factorisation
Division Method
Listing the Multiples
How to find the LCM of 18, 24 and 36 using the prime factorisation method?
In this method, we write the numbers as the product of prime factors to find the LCM
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
LCM (18, 24, 36) = 2 × 2 × 2 × 3 × 3 = 72
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