LCM of 17 and 19 is 323. It is very important to follow the best guide for effective learning of concepts. For this purpose, professional teachers prepared the article Least Common Multiple (LCM) in a comprehensive manner to promote a better conceptual understanding in students. Learning the LCM concept with the help of this article helps students speed up their problem-solving and time management skills which are vital from an exam perspective. Let us learn how to find the least common multiple of 17 and 19 using prime factorisation, division method and a list of multiples in this article.
What is LCM of 17 and 19?
The answer to this question is 323.
How to Find LCM of 17 and 19?
The LCM of 17 and 19 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 17 and 19 Using Prime Factorisation Method
In the prime factorisation method, the LCM of the two or more numbers is the product of the prime factors. Hence, the numbers 17 and 19 can be denoted as;
17 = 17
19 = 19
LCM (17, 19) = 17 × 19 = 323
LCM of 17 and 19 Using Division Method
In the division method, to find the LCM, we divide the numbers 17 and 19 by their prime factors until we get the result as one in the complete row. The product of these divisors illustrates the least common multiple of 17 and 19.
| 17 | 17 | 19 |
| 19 | 1 | 19 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (17, 19) = 17 × 19 = 323
LCM of 17 and 19 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 17 and 19 are as follows:
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, ……., 289, 306, 323, ……….
Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, ……, 285, 304, 323, ……….
LCM (17, 19) = 323
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 17 and 19?
Solution: 323 is the smallest number that is divisible by both 17 and 19.
2. The GCD and LCM of the two numbers are 1 and 323. If one number is 17, what is the other number?
Solution: Let the other number be m
We know that,
GCD × LCM = 17 × m
m = (GCD × LCM)/ 17
m = (1 × 323) / 17
m = 19
Hence the other number is 19.
Frequently Asked Questions on LCM of 17 and 19
What is the LCM of 17 and 19?
What is the LCM of 17 and 19 and the HCF of 17 and 19?
What are the common prime factors of 17 and 19?
Find the GCF if the LCM of 17 and 19 is 323.
GCF × LCM = 17 × 19
Given
LCM = 323
GCF × 323 = 17 × 19
GCF = 1
Write the methods used to find the LCM of 17 and 19.
The methods used to find the LCM of 17 and 19 are
Prime Factorisation
Division Method
Listing the Multiples
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