LCM of 14 and 91 is 182. The value which equally divides 14 and 91 determines the LCM. The common multiples of 14 and 91 will provide the least common multiple of 14 and 91. The multiples of 14 are (14, 28, 42, 56, 70, 84, ….) and the multiples of 91 are (91, 182, 273, 364, …..) respectively. For a proper understanding of the LCM concept and prime factorisation method, division method and listing of the multiples a thorough understanding of the steps is very crucial.
Also read: Least common multiple
What is LCM of 14 and 91?
The answer to this question is 182. The LCM of 14 and 91 using various methods are shown in this article for your reference. The LCM of two non-zero integers, 14 and 91, is the smallest positive integer 182 which is divisible by both 14 and 91 with no remainder.
How to Find LCM of 14 and 91?
LCM of 14 and 91 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 14 and 91 Using Prime Factorisation Method
The prime factorisation of 14 and 91, respectively, is given by:
14 = 2 x 7 = 2¹ x 7¹
91 = 7 x 13 = 7¹ x 13¹
LCM (14, 91) = 182
LCM of 14 and 91 Using Division Method
We’ll divide the numbers (14, 91) by their prime factors to get the LCM of 14 and 91 using the division method (preferably common). The LCM of 14 and 91 is calculated by multiplying these divisors.
|
2 |
14 |
91 |
|
7 |
7 |
91 |
|
13 |
1 |
13 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (14, 91) = 182
LCM of 14 and 91 Using Listing the Multiples
To calculate the LCM of 14 and 91 by listing out the common multiples, list the multiples as shown below.
Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, …..
Multiples of 91 = 91, 182, 273, 364, 455, 546, 637, …..
LCM (14, 91) = 182
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LCM of 14 and 91 Solved Examples
Question: What is the smallest number divisible by 14 and 91 exactly?
Solution:
The smallest number divisible by 14 and 91 exactly is LCM.
(14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, …..) are the multiples of 14
(91, 182, 273, 364, 455, 546, 637, …..) are the multiples of 91
Therefore, the LCM of 14 and 91 is 182.
Frequently Asked Questions on LCM of 14 and 91
Find the GCF if the LCM of 14 and 91 is 182.
We know that
LCM x GCF = 14 x 91
As LCM (14, 91) is 182
182 x GCF = 1274
GCF = 1274/182 = 7
Determine the LCM of 14 and 91.
Show the relation between GCF and LCM of 14 and 91.
The relation between GCF and LCM of 14 and 91 is:
LCM x GCF = 14 x 91
LCM x GCF = 1274
The LCM and GCD of two numbers are 182 and 7. If 14 is one number, find the other.
Consider the other number as y
GCD x LCM = 14 x y
y = (GCD x LCM)/14
y = (7 x 182)/14
y = 91
Hence, the other number is 91.
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