LCM of 9 and 14 is 126. LCM denotes the smallest positive number that is a multiple of two or more numbers. The article LCM with Examples is designed in an interesting way to enhance the problem-solving abilities of students. The concept is described in an easy to understand language based on the student’s understanding capacity. Learn how to calculate the least common multiple of 9 and 14 using prime factorisation, division method and a list of multiples here.
What is LCM of 9 and 14?
The Least Common Multiple of 9 and 14 is 126.
How to Find LCM of 9 and 14?
LCM of 9 and 14 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 9 and 14 Using Prime Factorisation Method
In the prime factorisation method, LCM of 9 and 14 can be obtained by multiplying prime factors raised to their respective highest power.
9 = 3 × 3
14 = 2 × 7
LCM (9, 14) = 2 × 3 × 3 × 7 = 126
LCM of 9 and 14 Using Division Method
In the division method, to find the LCM, we divide the numbers 9 and 14 by their prime factors until we get the result as one in the complete row. The product of these divisors shows the least common multiple of 9 and 14.
2 | 9 | 14 |
3 | 9 | 7 |
3 | 3 | 7 |
7 | 1 | 7 |
x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 14) = 2 × 3 × 3 × 7 = 126
LCM of 9 and 14 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to determine the least common multiple among them. Let us have a look at the multiples of 9 and 14 mentioned below.
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ………, 108, 117, 126, ………….
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ……….
LCM (9, 14) = 126
Related Articles
Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
![](https://cdn1.byjus.com/wp-content/uploads/2022/04/Application-of-LCM.jpg)
Solved Examples
1. What is the smallest number that is divisible by both 9 and 14?
Solution: 126 is the smallest number that is divisible by both 9 and 14.
2. What is the LCM if the product of two numbers is 126 and their GCD is 1?
Solution: Given
GCD = 1
Product of numbers = 126
We know that
GCF × LCM = Product of numbers
LCM = Product of numbers / GCF
LCM = 126 / 1
LCM = 126
Hence the LCM is 126.
Frequently Asked Questions on LCM of 9 and 14
What is the LCM of 9 and 14?
What are the methods used to find the least common multiple of 9 and 14?
The methods used to find the least common multiple of 9 and 14 are:
Prime Factorisation
Division method
Listing the Multiples
Is 116 the LCM of 9 and 14?
Mention the LCM of 9 and 14 and the HCF of 9 and 14.
The LCM of 9 and 14 is 126 and the HCF of 9 and 14 is 1.
If the LCM of 9 and 14 is 126. What is their GCF?
GCF × LCM = 9 × 14
Given
LCM = 126
GCF × 126 = 9 × 14
GCF = 1
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