13 and 169 LCM
LCM of 13 and 169 is equal to 169. The comprehensive work provides more insight of how to find what is the lcm of 13 and 169 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 13 and 169?
lcm (13 169) = (?)
13 => 13
169 => 13 x 13
= 13 x 13
= 169
lcm (13 and 169) = 169
169 is the lcm of 13 and 169.
where,
13 is a positive integer,
169 is a positive integer,
169 is the lcm of 13 and 169,
{13} in {13, 13 x 13} is the common factors of 13 and 169,
{13} in {13, 13 x 13} is the uncommon factors of 13 and 169.
Use in Mathematics: LCM of 13 and 169
The below are some of the mathematical applications where lcm of 13 and 169 can be used:
- to find the least number which is exactly divisible by 13 and 169.
- to find the common denominator for two fractions having 13 and 169 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 13 and 169 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 169 seconds repeatedly. The answer is that all bells A and B toll together at 169 seconds for the first time, at 338 seconds for the second time, at 507 seconds for the third time and so on.
Important Notes: 13 and 169 lcm
The below are the important notes to be remembered while solving the lcm of 13 and 169:
- The common prime factors and the remaining prime factors of 13 and 169 should be multiplied to find the least common multiple of 13 and 169, when solving lcm by using prime factors method.
- The results of lcm of 13 and 169, and the lcm of 169 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 169?
The below solved example with step by step work shows how to find what is the lcm of 13 and 169 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 13 and 169?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 13
B = 169
What to be found:
find the lcm of 13 and 169
step 2 Find the prime factors of 13 and 169:
Prime factors of 13 = 13
Prime factors of 169 = 13 x 13
step 3 Identify the repeated and non-repeated prime factors of 13 and 169:
{13} is the most repeated factor and {13} is the non-repeated factor of 13 and 169.
step 4 Find the product of repeated and non-repeated prime factors of 13 and 169:
= 13 x 13
= 169
lcm(13 and 169) = 169
Hence,
lcm of 13 and 169 is 169
This special division method is the easiest way to understand the entire calculation of what is the lcm of 13 and 169.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 13 and 169
What to be found:
lcm (13, 169) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
13 and 169
step 3 Choose the divisor which divides each or most of the given integers (13 and 169), 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 169 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 13 | 13 | 169 |
| 13 | 1 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 13 and 169:
= 13 x 13
= 169
LCM(13, 169) = 169
The least common multiple for two numbers 13 and 169 is 169