LCM of 14 and 18 is 126. The value evenly divisible by 14 and 18 gives you the LCM number. Least common multiples of 14 and 18 are found from the common multiples. (14, 28, 42, 56, 70, 84, ….) and (18, 36, 54, 72, 90,….) are the multiples of 14 and 18. The LCM of two numbers with the help of prime factorization, division and by listing the multiples are shown here for a good understanding among students.
Also read: Least common multiple
What is LCM of 14 and 18?
The answer to this question is 126. The LCM of 14 and 18 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 14 and 18, is the smallest positive integer 126 which is divisible by both 14 and 18 with no remainder.
How to Find LCM of 14 and 18?
LCM of 14 and 18 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 14 and 18 Using Prime Factorisation Method
The prime factorisation of 14 and 18, respectively, is given by:
14 = 2 x 7 = 2¹ x 7¹
18 = 2 x 3 x 3 = 2¹ x 3²
LCM (14, 18) = 126
LCM of 14 and 18 Using Division Method
We’ll divide the numbers (14, 18) by their prime factors to get the LCM of 14 and 18 using the division method (preferably common). The LCM of 14 and 18 is calculated by multiplying these divisors.
|
2 |
14 |
18 |
|
3 |
7 |
9 |
|
3 |
7 |
3 |
|
7 |
7 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (14, 18) = 126
LCM of 14 and 18 Using Listing the Multiples
To calculate the LCM of 14 and 18 by listing out the common multiples, list the multiples as shown below:
|
Multiples of 14 |
Multiples of 18 |
|
14 |
18 |
|
28 |
36 |
|
42 |
54 |
|
56 |
72 |
|
70 |
90 |
|
84 |
108 |
|
98 |
126 |
|
112 |
144 |
|
126 |
162 |
LCM (14, 18) = 126
Related Articles
Video Lesson on Applications of LCM
LCM of 14 and 18 Solved Examples
Question: Find the smallest number exactly divisible by 14 and 18.
Solution:
We know that;
The smallest number which is exactly divisible by 14 and 18 is the LCM.
Multiples of 14 = 14, 28, 42, 56, 70, …..
Multiples of 18 = 18, 36, 54, 72, 90, …..
Hence, the LCM of 14 and 18 is 126.
Frequently Asked Questions on LCM of 14 and 18
Find the LCM of 14 and 18 using the prime factorization method.
To find the LCM using the prime factorization, we first have to determine the prime factors.
14 = 2 x 7 = 2¹ x 7¹
18 = 2 x 3 x 3 = 2¹ x 3²
LCM of 14 and 18 is the product of prime factors raised to the highest exponent among the numbers 14 and 18
LCM of 14 and 18 = 126
If the LCM of 14 and 18 is 126, what is the GCF?
LCM x GCF = 14 x 18
Given
LCM of 14 and 18= 126
126 x GCF = 252
GCF = 252/126 = 2
What is the relation between GCF and LCM of 14 and 18?
The relation between GCF and LCM of 14 and 18 is
LCM x GCF = 14 x 18
LCM x GCF = 252
Comments