LCM of 14 and 24 is 168. The least common multiple is the method to find the smallest possible multiple of two or more numbers. Subject matter experts framed the article HCF and LCM in simple and understandable language so that students grasp the concepts easily. Following this article on a daily basis helps students to improve their skills required to secure high marks in exams. Let us learn a detailed explanation of how to find the least common multiple of 14 and 24 using different methods in this article.
What is LCM of 14 and 24?
The Least Common Multiple of 14 and 24 is 168.
How to Find LCM of 14 and 24?
We can find the LCM of 14 and 24 by using the methods given below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 14 and 24 Using Prime Factorisation Method
By prime factorisation method, the LCM of 14 and 24 can be obtained by multiplying prime factors raised to their respective highest power.
14 = 2 × 7
24 = 2 × 2 × 2 × 3
LCM (14, 24) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 14 and 24 Using Division Method
In the division method, we divide the numbers 14 and 45 by a common prime number until the remainder is a prime number or one. The product of these divisors represents the least common multiple of 14 and 24.
| 2 | 14 | 24 |
| 2 | 7 | 12 |
| 2 | 7 | 6 |
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (14, 24) = 2 × 2 × 2 × 3 × 7= 168
LCM of 14 and 24 Using Listing the Multiples
Here, we list the multiples of 14 and 24 to determine the least common multiple among them. Let us glance at the multiples of 14 and 24 given below.
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, ………….
Multiples of 24: 24, 48, 72, 96, 120, 144, 168, ……….
LCM (14, 24) = 168
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Prime Factorisation and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: The GCD and LCM of the two numbers are 2 and 168. If one number is 24, calculate the other number.
Solution: Let the other number be p
We know that,
GCD × LCM = 24 × p
p = (GCD × LCM) / 24
p = (2 × 168) / 24
p = 14
Hence the other number is 14.
Q. 2: Find the LCM of 14 and 24 using the prime factorisation method.
Solution: In this method, the given natural numbers are expressed as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree.
14 = 2 × 7
24 = 2 × 2 × 2 × 3
LCM (14, 24) = 2 × 2 × 2 × 3 × 7 = 168
Therefore the least common multiple of 14 and 24 by prime factorisation is 168.
Frequently Asked Questions on LCM of 14 and 24
What is the LCM of 14 and 24?
Is the LCM of 14 and 24 the same as the HCF of 14 and 24?
Is 188 the LCM of 14 and 24?
If the LCM of 14 and 24 is 168. What is their GCF?
GCF × LCM = 14 × 24
Given
LCM = 168
GCF × 168 = 14 × 24
GCF = 2
What are the methods used to determine the LCM of 14 and 24?
The methods used to determine the LCM of 14 and 24 are
Prime Factorisation
Division Method
Listing the Multiples
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