LCM of 39 and 65 is 195. The number which is divisible evenly by 39 and 65 helps to determine the LCM value. Least common multiples of 39 and 65 are found by considering the common multiples. (39, 78, 117, 156, 195, 234, 273, 312, 351, 390, ….) and (65, 130, 195, 260, 325, 390, 455, 520, 585, 650,….) are the multiples of 39 and 65. The LCM of two numbers according to the prime factorization, division and by listing the multiples are discussed here for a better knowledge of the basic Maths concepts among the students.
Also read: Least common multiple
What is LCM of 39 and 65?
The answer to this question is 195. The LCM of 39 and 65 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 39 and 65, is the smallest positive integer 195 which is divisible by both 39 and 65 with no remainder.
How to Find LCM of 39 and 65?
LCM of 39 and 65 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 39 and 65 Using Prime Factorisation Method
The prime factorisation of 39 and 65, respectively, is given by:
39 = 3 x 13 = 3¹ x 13¹
65 = 5 x 13 = 5¹ x 13¹
LCM (39, 65) = 195
LCM of 39 and 65 Using Division Method
We’ll divide the numbers (39, 65) by their prime factors to get the LCM of 39 and 65 using the division method (preferably common). The LCM of 39 and 65 is calculated by multiplying these divisors.
|
3 |
39 |
65 |
|
5 |
13 |
65 |
|
13 |
13 |
13 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (39, 65) = 195
LCM of 39 and 65 Using Listing the Multiples
To calculate the LCM of 39 and 65 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 39 |
Multiples of 65 |
|
39 |
65 |
|
78 |
130 |
|
117 |
195 |
|
156 |
260 |
|
195 |
325 |
LCM (39, 65) = 195
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 39 and 65 Solved Examples
Question: Determine the smallest number which is exactly divisible by 39 and 65.
Solution:
We know that
The smallest number which is exactly divisible by 39 and 65 is the LCM.
Multiples of 39 = 39, 78, 117, 156, 195, 234, 273, 312, 351, 390, ….
Multiples of 65 = 65, 130, 195, 260, 325, 390, 455, 520, 585, 650,….
Hence, the LCM of 39 and 65 is 195.
Frequently Asked Questions on LCM of 39 and 65
What is the LCM of 39 and 65 using the prime factorization method?
To find the LCM using the prime factorization, we should know the prime factors.
39 = 3 x 13
65 = 5 x 13
LCM of 39 and 65 is the product of prime factors raised to the highest exponent among the numbers 39 and 65
LCM of 39 and 65 = 195
If the LCM of 39 and 65 is 195, find the GCF.
LCM x GCF = 39 x 65
Given
LCM of 39 and 65 = 195
195 x GCF = 2535
GCF = 2535/195 = 13
Show the relation between GCF and LCM of 39 and 65.
The relation between GCF and LCM of 39 and 65 is
LCM x GCF = 39 x 65
LCM x GCF = 2535
For two numbers, LCM = 195 and GCF = 13. If one number is 65, what is the other?
Consider z as the other number
GCF x LCM = 65 x y
y = (GCF x LCM)/ 65
y = (13 x 195)/65
y = 39
Hence, the other number is 39.
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