LCM of 9 and 16 is 144. The smallest number among all common multiples of 9 and 16 is 144. We can determine the LCM of 9 and 16 with the help of prime factorisation, division method and listing multiples. (9, 18, 27, 36, 45, 54, 63, ….) and (16, 32, 48, 64, 80, 96….) are the first few multiples of 9 and 16. Students can make use of the article HCF and LCM to learn tricks of finding LCM and HCF more effectively. Let us grasp the technique of finding the least common multiple of 9 and 16 with examples and FAQs in a comprehensive manner in this article.
What is LCM of 9 and 16?
The Least Common Multiple of 9 and 16 is 144.
How to Find LCM of 9 and 16?
The following methods help us to find the LCM of 9 and 16:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 16 Using Prime Factorisation Method
By prime factorisation method, we can write 9 and 16 as the product of prime numbers, such that;
9 = 3 × 3
16 = 2 × 2 × 2 × 2
LCM (9, 16) = 2 × 2 × 2 × 2 × 3 × 3 = 144
LCM of 9 and 16 Using Division Method
Here, we divide the numbers 9 and 16 by their prime factors to find their LCM. The product of these divisors represents the least common multiple of 9 and 16.
| 2 | 9 | 16 |
| 2 | 9 | 8 |
| 2 | 9 | 4 |
| 2 | 9 | 2 |
| 3 | 9 | 1 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No more further division can be done.
Therefore, LCM (9, 16) = 2 × 2 × 2 × 2 × 3 × 3 = 144
LCM of 9 and 16 Using Listing the Multiples
To determine the least common multiple of 9 and 16 using listing multiples, we list out the multiples of 9 and 16 as shown below.
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ……., 126, 135, 144, ……..
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ……..
LCM (9, 16) = 144
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: Find the LCM of 9 and 16 using listing multiples?
Solution: First, list the multiples of 9 and 16
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, …..
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, ……..
Here, the LCM is 144
Hence the LCM of 9 and 16 is 144.
Q. 2: The product of two numbers is 144. If their GCD is 1, calculate their LCM.
Solution: Given
GCD = 1
Product of numbers = 144
We know that,
LCM × GCD = Product of numbers
LCM = Product of numbers/GCD
LCM = 144/1
LCM = 144
Thus the LCM is 144.
Frequently Asked Questions on LCM of 9 and 16
What is the LCM of 9 and 16?
How do you find the LCM of 9 and 16 by Prime Factorisation?
9 = 3 × 3
16 = 2 × 2 × 2 × 2
LCM (9, 16) = 2 × 2 × 2 × 2 × 3 × 3 = 144
Hence the LCM of 9 and 16 is 144.
Name the methods used to determine the LCM of 9 and 16.
The following methods are used to determine the LCM of 9 and 16
Prime Factorisation Method
Division Method
Listing the Multiples
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