LCM of 9 and 36 is 36. The smallest number among all common multiples of 9 and 36 is the LCM of 9 and 36. (9, 18, 27, 36, 45, etc.) and (36, 72, 108, 144, etc.) are the first few multiples of 9 and 36, respectively. To find the LCM of Two Numbers that is 9 and 36, there are three main methods: listing multiples, division method, and prime factorization.
What is LCM of 9 and 36?
The answer to this question is 36. The LCM of 9 and 36 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 36, is the smallest positive integer 36 which is divisible by both 9 and 36 with no remainder.
Also read: Least common multiple
How to Find LCM of 9 and 36?
LCM of 9 and 36 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 36 Using Prime Factorisation Method
The prime factorisation of 9 and 36, respectively, is given by:
9 = (3 × 3) = 32 and
36 = (2 × 2 × 3 × 3) = 22 × 32
LCM (9, 36) = 36
LCM of 9 and 36 Using Division Method
We’ll divide the numbers (9, 36) by their prime factors to get the LCM of 9 and 36 using the division method (preferably common). The LCM of 9 and 36 is calculated by multiplying these divisors.
2 | 9 | 36 |
2 | 9 | 18 |
3 | 9 | 9 |
3 | 3 | 3 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 36) = 2 x 2 x 3 x 3 = 36
LCM of 9 and 36 Using Listing the Multiples
To calculate the LCM of 9 and 36 by listing out the common multiples, list the multiples as shown below
Multiples of 9 | Multiples of 36 |
9 | 36 |
18 | 72 |
27 | 108 |
36 | 144 |
45 | – |
The smallest common multiple of 9 and 36 is 36.
LCM (9, 36) = 36
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LCM of 9 and 36 Solved Example
Question: The product of two numbers is 324. If their GCD is 9, what is their LCM?
Solution:
Given: GCD = 9
product of numbers = 324
LCM × GCD = product of numbers
LCM = Product/GCD = 324/9
Therefore, the LCM is 36.
The probable combination for the given case is LCM(9, 36) = 36.
Frequently Asked Questions on LCM of 9 and 36
What is the LCM of 9 and 36?
List the methods used to find the LCM of 9 and 36.
How to Find the LCM of 9 and 36 by Prime Factorization?
LCM of 9, 36 = 22 × 32 = 36.
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