LCM of 3 and 17 is 51. The least common multiple of 3 and 17 can be found using the common multiples. (3, 6, 9, 12, 15, 18, 21, ….) and (17, 34, 51, 68, 85, 102,….) are the multiples of 3 and 17. To determine the LCM of two numbers, methods such as prime factorisation, by listing the multiples and division, can be used, using the materials given at BYJU’S.
Also read: Least common multiple
What is LCM of 3 and 17?
The answer to this question is 51. The LCM of 3 and 17 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 17, is the smallest positive integer 51 which is divisible by both 3 and 17 with no remainder.
How to Find LCM of 3 and 17?
LCM of 3 and 17 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3 and 17 Using Prime Factorisation Method
The prime factorisation of 3 and 17, respectively, is given by:
3 = 3¹
17 = 17¹
LCM (3, 17) = 51
LCM of 3 and 17 Using Division Method
We’ll divide the numbers (3, 17) by their prime factors to get the LCM of 3 and 17 using the division method (preferably common). The LCM of 3 and 17 is calculated by multiplying these divisors.
|
3 |
3 |
17 |
|
17 |
1 |
17 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (3, 17) = 51
LCM of 3 and 17 Using Listing the Multiples
To calculate the LCM of 3 and 17 by listing out the common multiples, list the multiples as shown below.
- Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 45, 48, 51, . . . .
- Multiples of 17 = 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, …….
The smallest common multiple of 3 and 17 is 51.
Therefore, LCM (3, 17) = 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 3 and 17 Solved Examples
Question: If the LCM is 51 and GCD is 1, determine the other number when one number is 17.
Solution:
Consider p as the other number
GCD x LCM = 17 x p
p = (GCD x LCM)/17
p = (1 x 51)/ 17
p = 3
Hence, the other number is 3.
Frequently Asked Questions on LCM of 3 and 17
What is the LCM of 3 and 17?
What methods are used to find the LCM of 3 and 17?
If the LCM of 3 and 17 is 51, find the GCF.
LCM x GCF = 3 x 17
Given
LCM of 3 and 17 = 51
51 x GCF = 51
GCF = 51/51 = 1
With the help of prime factorisation, find the LCM of 3 and 17.
With the help of prime factorisation,
3 = 3¹
17 = 17¹
LCM of 3 and 17 is 51.
Write the relation between LCM and GCF of 3 and 17.
The relation between LCM and GCF of 3 and 17 is
LCM x GCF = 3 x 17
LCM x GCF = 51
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