LCM of 12, 15 and 18 is 180. The LCM is the technique to determine the least common multiple between any two or more numbers. The article Prime Factorisation and Division Method for LCM and HCF has been developed by the experts in an easy and understandable manner to help students in finding the least common multiple and highest common factors of given numbers in the most efficient possible ways. Referring to this article while solving problems on a daily basis enables students to score good marks in exams. Let us learn how to find the least common multiple of 12, 15 and 18 in a precise manner here.
What is LCM of 12, 15 and 18?
The Least Common Multiple of 12, 15 and 18 is 180.
How to Find LCM of 12, 15 and 18?
The following methods are used to find the LCM of 12, 15 and 18:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 12, 15 and 18 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 12, 15 and 18 are written as;
12 = 2 × 2 × 3
15 = 3 × 5
18 = 2 × 3 × 3
LCM (12, 15, 18) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 12, 15 and 18 Using Division Method
In this method, we divide the numbers 12, 15 and 18 by a common prime number until the remainder is a prime number or one. The product of these divisors shows the least common multiple of 12, 15 and 18.
| 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 more further division can be done.
Hence, LCM (12, 15, 18) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 12, 15 and 18 Using Listing the Multiples
In this method, we list down the multiples of 12, 15 and 18 to find the least common multiple among them. The multiples of 12, 15 and 18 are shown below.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120,……….., 156, 168, 180, ……..
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, ………..
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, …………
LCM (12, 15, 18) = 180
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Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by 12, 15,18 exactly?
Solution: 180 is the smallest number that is divisible by 12, 15,18 exactly.
2. What is the lowest common factor of 12, 15 and 18?
Solution: 180 is the lowest common factor of 12, 15 and 18.
Frequently Asked Questions on LCM of 12, 15 and 18
What is the LCM of 12, 15 and 18?
Is the LCM of 12, 15 and 18 the same as the HCF of 12, 15 and 18?
List the methods used to find the LCM of 12, 15 and 18.
The methods used to find the LCM of 12, 15 and 18 are as follows:
Prime Factorisation
Division method
Listing the Multiples
Find the LCM of 12, 15 and 18 by prime factorisation method.
To find the LCM by prime factorisation, we express the numbers as the product of prime factors
12 = 2 × 2 × 3
15 = 3 × 5
18 = 2 × 3 × 3
LCM (12, 15, 18) = 2 × 2 × 3 × 3 × 5 = 180
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