LCM of 13 and 17 is 221. The least common multiple can be defined as the smallest common multiple of two or more numbers. Least Common Multiple (LCM) is prepared by experts in a simple and understandable language to help students in finding the lowest common multiple of given numbers in an efficient manner. This article is the best reference guide for the students, which helps them to obtain better conceptual knowledge. Let us learn how to verify the least common multiple of 13 and 17 using examples and FAQs in this article.
What is LCM of 13 and 17?
The Least Common Multiple of 13 and 17 is 221.
How to Find LCM of 13 and 17?
LCM of 13 and 17 can be determined using three methods
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 13 and 17 Using Prime Factorisation Method
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.
13 = 13
17 = 17
LCM (13, 17) = 13 × 17= 221
LCM of 13 and 17 Using Division Method
In the division method, to calculate the least common multiple of 13 and 17, we divide the numbers 13 and 17 by their prime factors until we get the result as one in the complete row. The product of these divisors depicts the least common multiple of 13 and 17.
| 13 | 13 | 17 |
| 17 | 1 | 17 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (13, 17) = 13 × 17 = 221
LCM of 13 and 17 Using Listing the Multiples
In this method, we list out the multiples of given numbers to find the least common multiple. Let us have a look at the multiples of 13 and 17 given below.
Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, ……., 195, 208, 221, ………
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, ………….
LCM (13, 17) = 221
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 13 and 17?
Solution: 221 is the smallest number that is divisible by both 13 and 17.
Q. 2: The GCD and LCM of the two numbers are 1 and 221. If one number is 17, calculate the other number.
Solution: Let the other number be q
We know that,
(GCD × LCM) = 17 × q
q = (GCD × LCM) / 17
q = (1 × 221) / 17
q = 13
Hence the other number is 13.
Frequently Asked Questions on LCM of 13 and 17
What is the LCM of 13 and 17?
Is the LCM of 13 and 17 the same as the HCF of 13 and 17?
121 is the LCM of 13 and 17. True or False.
Find the GCF if the LCM of 13 and 17 is 221.
GCF × LCM = 13 × 17
Given
LCM = 221
GCF × 221 = 13 × 17
GCF = 1
Mention the relation between GCF and LCM of 13 and 17.
The relation between GCF and LCM of 13 and 17 is
GCF × LCM = 13 × 17
GCF × LCM = 221
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