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
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
Comments