LCM of 13 and 16
208 is the LCM of 13 and 16. The step-by-step solution using prime factors and special division methods is one of the simple methods to easily understand how to find what is the LCM of 13 and 16, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 13 and 16?
lcm (13 16) = (?)
13 => 13
16 => 2 x 2 x 2 x 2
= 13 x 2 x 2 x 2 x 2
= 208
lcm (13 and 16) = 208
208 is the LCM of 13 and 16.
where,
13 is a positive integer,
16 is a positive integer,
208 is the LCM of 13 and 16,
There is no common factors of 13 and 16 in {13, 2 x 2 x 2 x 2},
{13 x 2 x 2 x 2 x 2} in {13, 2 x 2 x 2 x 2} are the uncommon factors of 13 and 16.
Use in Mathematics: LCM of 13 and 16
The below are some of the mathematical applications where lcm of 13 and 16 can be used:
- to find the least number which is exactly divisible by 13 and 16.
- to find the common denominator for two fractions having 13 and 16 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 13 and 16 helps to find the exact time when two similar and recurring events with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time the bells A and B all toll together, if bell A tolls at 13 seconds and bell B tolls at 16 seconds repeatedly. The answer is that all bells A and B toll together at 208 seconds for the first time, at 416 seconds for the second time, at 624 seconds for the third time and so on.
Important Notes: 13 and 16 lcm
The below are the important notes to be remembered while solving the lcm of 13 and 16:
- The common prime factors and the remaining prime factors of 13 and 16 should be multiplied to find the least common multiple of 13 and 16, when solving lcm by using prime factors method.
- The results of lcm of 13 and 16, and the lcm of 16 and 13 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 13 and 16?
The below solved example with step by step work shows how to find what is the lcm of 13 and 16 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 13 and 16?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 13
B = 16
What to be found:
find the lcm of 13 and 16
step 2 Find the prime factors of 13 and 16:
Prime factors of 13 = 13
Prime factors of 16 = 2 x 2 x 2 x 2
step 3Identify the repeated and non-repeated prime factors of 13 and 16:
Since there is no common factors between 13 and 16, multiplying the given numbers directly provides the LCM of
13 and 16.
= 13 x 16
= 208
lcm(13 and 16) = 208
Hence,
lcm of 13 and 16 is 208
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 13 and 16.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 13 and 16
What to be found:
lcm (13, 16) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
13 and 16
step 3 Choose the divisor which divides each or most of the given integers (13 and 16), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 13 and 16 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 13 | 16 |
| 2 | 13 | 8 |
| 2 | 13 | 4 |
| 2 | 13 | 2 |
| 13 | 13 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 13 and 16:
= 2 x 2 x 2 x 2 x 13
= 208
LCM(13, 16) = 208
The LCM of two numbers 13 and 16 is 208