LCM of 39 and 65

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.

lcm of 39 and 65

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

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

Q1

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

Q2

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

Q3

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

Q4

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.

Q5

What are the methods used to find the LCM of 39 and 65?

The methods used to find the LCM of 39 and 65 are prime factorisation, division and listing the multiples.

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