LCM of 36 and 90 is 180. The least common multiple denotes the smallest positive integer which is multiple in a given set of numbers. For comprehensive solutions based on the LCM concept, students must follow the article Least Common Multiple (LCM) prepared by highly professional teachers. Learning the LCM concept by referring to this article undoubtedly improves conceptual knowledge among the students. Let us learn the simple way to find the least common multiple of 36 and 90 using prime factorisation, division method and a list of multiples in this article.
What is LCM of 36 and 90?
The Least Common Multiple of 36 and 90 is 180.
How to Find LCM of 36 and 90?
The LCM of 36 and 90 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 36 and 90 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 36 and 90 can be expressed as;
36 = 2 × 2 × 3 × 3
90 = 2 × 3 × 3 × 5
LCM (36, 90) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 36 and 90 Using Division Method
In the division method, we divide the numbers 36 and 90 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 36 and 90.
| 2 | 36 | 90 |
| 2 | 18 | 45 |
| 3 | 9 | 45 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (36, 90) = 2 × 2 × 3 × 3 × 5 = 180
LCM of 36 and 90 Using Listing the Multiples
Here, we list down the multiples of each number until the first common multiple is found among them. The below table shows the multiples of 36 and 90.
| Multiples of 36 | Multiples of 90 |
| 36 | 90 |
| 72 | 180 |
| 108 | 270 |
| 144 | 360 |
| 180 | 450 |
| 216 | 540 |
LCM (36, 90) = 180
Related Articles
Prime Factorisation 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 both 36 and 90?
Solution: 180 is the smallest number that is divisible by both 36 and 90.
2. The GCD and LCM of the two numbers are 18 and 180. If one number is 90, what is the other number?
Solution: Let the other number be p
We know that
GCD × LCM = 90 × p
p = (GCD × LCM) / 90
p = (18 × 180) / 90
p = 36
Therefore the other number is 36.
Frequently Asked Questions on LCM of 36 and 90
What is the LCM of 36 and 90?
What is the difference between the LCM of 36 and 90 and the HCF of 36 and 90?
What are the methods used to find the LCM of 36 and 90?
The following methods are used to find the LCM of 36 and 90
Prime Factorisation
Division method
Listing of Multiples
Find the GCF if the LCM of 36 and 90 is 180.
GCF × LCM = 36 × 90
Given
LCM = 180
GCF × 180 = 36 × 90
GCF = 18
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