LCM of 17 and 51 is 51. The number evenly divisible by 17 and 51 gives the LCM value. Least common multiples of 17 and 51 are found by using the common multiples. (17, 34, 51, 68, 85, 102, 119, ….) and (51, 102, 153, 204, 255,….) are the multiples of 17 and 51. The LCM of two numbers with the help of prime factorization, division and by listing the multiples are discussed in a stepwise format here for a better knowledge of fundamental concepts among the students.
Also read: Least common multiple
What is LCM of 17 and 51?
The answer to this question is 51. The LCM of 17 and 51 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 17 and 51, is the smallest positive integer 51 which is divisible by both 17 and 51 with no remainder.
How to Find LCM of 17 and 51?
LCM of 17 and 51 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 17 and 51 Using Prime Factorisation Method
The prime factorisation of 17 and 51, respectively, is given by:
17 = 17 = 5¹
51 = 3 x 17 = 3¹ x 17¹
LCM (17, 51) = 51
LCM of 17 and 51 Using Division Method
We’ll divide the numbers (17, 51) by their prime factors to get the LCM of 17 and 51 using the division method (preferably common). The LCM of 17 and 51 is calculated by multiplying these divisors.
|
3 |
17 |
51 |
|
17 |
17 |
17 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (17, 51) = 51
LCM of 17 and 51 Using Listing the Multiples
To calculate the LCM of 17 and 51 by listing out the common multiples, list the multiples as shown below
|
Multiples of 17 |
Multiples of 51 |
|
17 |
51 |
|
34 |
102 |
|
51 |
153 |
|
68 |
204 |
LCM (17, 51) = 51
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 17 and 51 Solved Examples
Question: What is the smallest number which is exactly divisible by 17 and 51?
Solution:
We know that
The smallest number which is exactly divisible by 17 and 51 is the LCM.
Multiples of 17 = 17, 34, 51, 68, 85, 102, 119, ….
Multiples of 51 = 51, 102, 153, 204, 255, 306, 357,….
Hence, the LCM of 17 and 51 is 51.
Frequently Asked Questions on LCM of 17 and 51
What is the LCM of 17 and 51 using the prime factorization method?
To find the LCM using the prime factorization, we should know the prime factors.
17 = 17 = 5¹
51 = 3 x 17 = 3¹ x 17¹
LCM of 17 and 51 is the product of prime factors raised to the highest exponent among the numbers 17 and 51
LCM of 17 and 51 = 51
If the LCM of 17 and 51 is 51, find the GCF.
LCM x GCF = 17 x 51
Given
LCM of 17 and 51 = 51
51 x GCF = 867
GCF = 867/51 = 17
Show the relation between GCF and LCM of 17 and 51.
The relation between GCF and LCM of 17 and 51 is
LCM x GCF = 17 x 51
LCM x GCF = 867
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