LCM of 13 and 16 is 208. The LCM value is the common multiple which is divisible evenly by the given two numbers. Least common multiple of 13 and 16 is the smallest number we get from the common multiples. (13, 26, 39, 52, 65, ….) and (16, 32, 48, 64, 80,….) are the first few multiples of 13 and 16. Few methods like division, prime factorisation and listing of multiples are used to determine the LCM.
Also read: Least common multiple
What is LCM of 13 and 16?
The answer to this question is 208. The LCM of 13 and 16 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 13 and 16, is the smallest positive integer 208 which is divisible by both 13 and 16 with no remainder.
How to Find LCM of 13 and 16?
LCM of 13 and 16 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 13 and 16 Using Prime Factorisation Method
The prime factorisation of 13 and 16, respectively, is given by:
13 = 13 = 13¹
16 = 2 x 2 x 2 x 2 = 2⁴
LCM (13, 16) = 208
LCM of 13 and 16 Using Division Method
We’ll divide the numbers (13, 16) by their prime factors to get the LCM of 13 and 16 using the division method (preferably common). The LCM of 13 and 16 is calculated by multiplying these divisors.
|
2 |
13 |
16 |
|
2 |
13 |
8 |
|
2 |
13 |
4 |
|
2 |
13 |
2 |
|
13 |
13 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (13, 16) = 208
LCM of 13 and 16 Using Listing the Multiples
To calculate the LCM of 13 and 16 by listing out the common multiples, list the multiples as shown below
- Multiples of 13 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, . . . ., 182, 195, 208, . . . .
- Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, . . . ., 144, 160, 176, 192, 208, . . . .
LCM (13, 16) = 208
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LCM of 13 and 16 Solved Examples
Question: The LCM and GCD of two numbers are 208 and 1 respectively. If one of the numbers is 16, find the other.
Solution:
Consider a as the other number.
GCD x LCM = 16 x a
a = (GCD x LCM)/ 16
a = (1 x 208)/16
a = 13
Hence, the other number is 13.
Frequently Asked Questions on LCM of 13 and 16
Find the LCM of 13 and 16.
Which methods can be used to find the LCM of 13 and 16?
Calculate the GCF if the LCM of 13 and 16 is 208.
LCM x GCF = 13 x 16
Given
LCM of 13 and 16 = 208
208 x GCF = 208
GCF = 208/208 = 1
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