LCM of 12 and 45 is 180. LCM represents the smallest positive number which is a multiple of two or more numbers. It is essential to master the LCM concept to obtain proficiency in determining the least common multiple of given numbers. The article Prime Factorisation and Division Method for LCM and HCF helps students to solve the problems based on the LCM and HCF with speed and accuracy. Here, we will discuss how to find the least common multiple of 12 and 45 in detail.
What is LCM of 12 and 45?
The answer to this question is 180.
How to Find LCM of 12 and 45?
LCM of 12 and 45 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 12 and 45 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 12 and 45 can be expressed as;
12 = 2 × 2 × 3
45 = 3 × 3 × 5
LCM (12, 45) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 12 and 45 Using Division Method
In this method, we divide the numbers 12 and 45 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 12 and 45.
| 2 | 12 | 45 |
| 2 | 6 | 45 |
| 3 | 3 | 45 |
| 3 | 1 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 45) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 12 and 45 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 12 and 45 are mentioned below.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ………., 156, 168, 180, ……….
Multiples of 45: 45, 90, 135, 180, …………..
LCM (12, 45) = 180
Related Articles
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 12 and 45?
Solution: 180 is the smallest number that is divisible by both 12 and 45.
2. The GCD and LCM of the two numbers are 3 and 180. If one number is 12, what is the other number?
Solution: Let the other number be p
We know that,
GCD × LCM = 12 × p
p = (GCD × LCM) / 12
p = (3 × 180) / 12
p = 45
Hence the other number is 45.
Frequently Asked Questions on LCM of 12 and 45
What is the LCM of 12 and 45?
Is the LCM of 12 and 45 the same as the HCF of 12 and 45?
Is 190 the LCM of 12 and 45?
What are the methods used to find the LCM of 12 and 45?
The methods used to find the LCM of 12 and 45 are
Prime Factorisation
Division Method
Listing the Multiples
Mention the relation between GCF and LCM of 12 and 45.
The equation used to denote the relation between GCF and LCM of 12 and 45 is
GCF × LCM = 12 × 45
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