LCM of 19 and 57 is 57. The method to find the smallest common multiple between any two or more numbers is known as the least common multiple. Students are advised to use the article Least Common Multiple (LCM) prepared by experts to obtain in-depth knowledge of LCM. Prime factorisation, division method and listing multiples are the three methods used to determine the LCM of given numbers. Let us understand how to find the least common multiple of 19 and 57 with solved examples and FAQs in a comprehensive manner in this article.
What is LCM of 19 and 57?
The answer to this question is 57.
How to Find LCM of 19 and 57?
The following methods are used to find the LCM of 19 and 57:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 19 and 57 Using Prime Factorisation Method
By prime factorisation method, we can write 19 and 57 as the product of prime numbers, such that;
19 = 19
57 = 3 × 19
LCM (19, 57) = 3 × 19 = 57
LCM of 19 and 57 Using Division Method
Here, we divide the numbers 19 and 57 by their prime factors to determine their LCM. The product of these divisors represents the least common multiple of 19 and 57.
|
3 |
19 |
57 |
|
19 |
19 |
19 |
|
x |
1 |
1 |
No more further division can be done.
Hence, LCM (19, 57) = 3 × 19 = 57
LCM of 19 and 57 Using Listing the Multiples
To determine the least common multiple of 19 and 57 using listing multiples, we list out the multiples of 19 and 57 as shown below.
|
Multiples of 19 |
Multiples of 57 |
|
19 |
57 |
|
38 |
114 |
|
57 |
171 |
|
76 |
228 |
|
95 |
285 |
|
114 |
342 |
LCM (19, 57) = 57
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: Calculate the smallest number that is divisible by 19 and 57.
Solution: The LCM of 19 and 57 is the smallest number that is divisible by 19 and 57
Multiples of 19 = 19, 38, 57, 76, 95, 114, ….
Multiples of 57 = 57, 114, 171, 228, 285, 342,…..
Thus the LCM of 19 and 57 is 57.
Q. 2: The GCD and LCM of the two numbers are 19 and 57 respectively. If one number is 19, calculate the other number.
Solution: Let the other number be y.
GCD × LCM = 19 × y
y = (GCD × LCM) / 19
y = (19 × 57) / 19
y = 57
Hence the other number is 57.
Frequently Asked Questions on LCM of 19 and 57
Write the LCM of 19 and 57.
What are the methods used to find the LCM of 19 and 57?
The methods used to find the LCM of 19 and 57 are as follows:
Prime Factorisation
Division Method
Listing the multiples
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