The Least Common Multiple (LCM) of 9 and 36 is 36. This is the smallest number that is a common multiple of both 9 and 36. The first few multiples of 9 are 9, 18, 27, 36, 45, and so on. The multiples of 36 are 36, 72, 108, 144, etc. There are several methods to find the LCM of two numbers like 9 and 36, including listing multiples, using the division method, and prime factorization.
LCM of 9 and 36 - Methods and Solved Examples | Testbook.com
Last Updated on May 30, 2024
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Understanding the LCM of 9 and 36
The LCM of the numbers 9 and 36 is 36. This article will guide you through how to calculate the LCM of these two numbers using various methods. The LCM of two non-zero integers, like 9 and 36, is the smallest positive integer (in this case, 36) that can be divided by both numbers without leaving any remainder.
Also read: What is the Least Common Multiple?
Methods to Calculate the LCM of 9 and 36
There are three primary methods to calculate the LCM of 9 and 36:
- Prime Factorisation
- Division method
- Listing the multiples
Using Prime Factorisation to Find the LCM of 9 and 36
The prime factorisation of 9 is 3 × 3, while for 36, it's 2 × 2 × 3 × 3. Therefore, the LCM of 9 and 36 is 36.
Finding the LCM of 9 and 36 Using the Division Method
For this method, we divide the numbers 9 and 36 by their common prime factors. The LCM is then calculated by multiplying these divisors. Let's see how it works in the table below.
| 2 | 9 | 36 |
| 2 | 9 | 18 |
| 3 | 9 | 9 |
| 3 | 3 | 3 |
| x | 1 | 1 |
The LCM of 9 and 36 is the product of these divisors, which is 36.
Finding the LCM of 9 and 36 by Listing the Multiples
Another way to find the LCM of 9 and 36 is by listing out the multiples of each number and identifying the smallest common multiple.
| Multiples of 9 | Multiples of 36 |
| 9 | 36 |
| 18 | 72 |
| 27 | 108 |
| 36 | 144 |
| 45 | – |
Here, we can see that the smallest common multiple of 9 and 36 is 36. Therefore, the LCM of 9 and 36 is 36.
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Frequently Asked Questions
What is the LCM of 9 and 36?
The LCM of 9 and 36 is 36. To find the least common multiple of 9 and 36, we need to find the multiples of 9 and 36 (multiples of 9 = 9, 18, 27, 36; multiples of 36 = 36, 72, 108, 144) and choose the smallest multiple that is exactly divisible by 9 and 36, i.e., 36.
List the methods used to find the LCM of 9 and 36.
The methods used to find the LCM of 9 and 36 are the Prime Factorization Method, Division Method and Listing multiples.
How to Find the LCM of 9 and 36 by Prime Factorization?
To find the LCM of 9 and 36 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (36 = 2 × 2 × 3 × 3). LCM of 9 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 36. LCM of 9, 36 = 22 × 32 = 36.
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