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LCM of 13 and 15

LCM of 13 and 15 is 195. The value evenly divisible by the numbers 13 and 15 gives the LCM. The Least common multiple of 13 and 15 can be found from the multiples which are common in the given numbers. The multiples of 13 are (13, 26, 39, 52, ….) and the multiples of 15 are (15, 30, 45, 60, 75, 90, 105, ….) respectively. Prime factorisation, listing of the multiples and division are the few methods used to find the LCM.

Also read: Least common multiple

What is LCM of 13 and 15?

The answer to this question is 195. The LCM of 13 and 15 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 13 and 15, is the smallest positive integer 195 which is divisible by both 13 and 15 with no remainder.

lcm of 13 and 15

How to Find LCM of 13 and 15?

LCM of 13 and 15 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 13 and 15 Using Prime Factorisation Method

The prime factorisation of 13 and 15, respectively, is given by:

13 = 13¹

15 = 3 x 5 = 3¹ x 5¹

LCM (13, 15) = 195

LCM of 13 and 15 Using Division Method

We’ll divide the numbers (13, 15) by their prime factors to get the LCM of 13 and 15 using the division method (preferably common). The LCM of 13 and 15 is calculated by multiplying these divisors.

3 13 15
5 13 5
13 1 1
x 1 1

No further division can be done. 

Hence, LCM (13, 15) = 195

LCM of 13 and 15 Using Listing the Multiples

To calculate the LCM of 13 and 15 by listing out the common multiples, list the multiples as shown below

Multiples of 13 Multiples of 15
13 15
26 30
39 45
52 60
65 75
78 90
91 105
104 120
117 135
130 150
143 165
156 180
169 195
182 210
195 225
208 240

LCM (13, 15) = 195

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Video Lesson on Applications of LCM

LCM of 13 and 15 Solved Examples 

If the LCM and GCD of two numbers are 195 and 1 respectively, calculate the other number if one number is 15.

Solution:

Consider the number as z

We know that

GCD x LCM = 15 x z

z = (GCD x LCM)/15

Substituting the values

z = (195 x 1)/15

z = 13

Hence, the other number is 13.

Frequently Asked Questions on LCM of 13 and 15

What is the LCM of 13 and 15?

The LCM of 13 and 15 is 195.

Find GCF if the LCM of 13 and 15 is 195.

LCM x GCF = 13 x 15

Given

LCM of 13 and 15 is 195

195 x GCF = 195

GCF = 195/195 = 1

What are the methods used to find the LCM of 13 and 15?

The methods used to find the LCM of 13 and 15 are Prime Factorisation, Division method and Listing the multiples

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