The LCM of 13 and 14 is 182. LCM represents the smallest positive number which is a multiple of two or more numbers. The in-depth explanation of the concept present in the article Least Common Multiple (LCM) helps students in building time management skills and also boosts their confidence level in achieving high marks in exams. Students must practise the problems by referring to the article designed by experts to understand the concept in an efficient manner. In this article, let us grasp the simple method of calculating the least common multiple of 13 and 14.
What is LCM of 13 and 14?
The answer to this question is 182.
How to Find LCM of 13 and 14?
LCM of 13 and 14 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 13 and 14 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence, the numbers 13 and 14 can be expressed as;
13 = 13
14 = 2 × 7
LCM (13, 14) = 2 × 7 × 13 = 182
LCM of 13 and 14 Using Division Method
In this method, we divide the numbers 13 and 14 by a common prime number until the remainder is a prime number or one. The product of these divisors denotes the least common multiple of 13 and 14.
| 2 | 13 | 14 |
| 7 | 13 | 7 |
| 13 | 13 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (13, 14) = 2 × 7 × 13 = 182
LCM of 13 and 14 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 13 and 14 are mentioned below.
Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, ………..
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, ………….
LCM (13, 14) = 182
Related Articles
Prime Factorization 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 13 and 14?
Solution: 182 is the smallest number that is divisible by both 13 and 14.
2. The GCD and LCM of two numbers are 1 and 182. If one number is 13, calculate the other number.
Solution: Let the other number be k
We know that,
GCD × LCM = 13 × k
k = (GCD × LCM) / 13
k = (1 × 182) / 13
k = 14
Hence, the other number is 14.
Frequently Asked Questions on LCM of 13 and 14
What is the LCM of 13 and 14?
What is the difference between the LCM of 13 and 14 and the HCF of 13 and 14?
Is 180 the LCM of 13 and 14?
Find the GCF if the LCM of 13 and 14 is 182.
GCF × LCM = 13 × 14
Given
LCM = 182
GCF × 182 = 13 × 14
GCF = 1
Calculate the LCM of 13 and 14 using the prime factorisation method.
To find the LCM, we write the numbers as the product of prime factors
13 = 13
14 = 2 × 7
LCM (13, 14) = 2 × 7 × 13 = 182
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