13 and 117 LCM
LCM of 13 and 117 is equal to 117. The comprehensive work provides more insight of how to find what is the lcm of 13 and 117 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 117?
lcm (13 117) = (?)
13 => 13
117 => 3 x 3 x 13
= 13 x 3 x 3
= 117
lcm (13 and 117) = 117
117 is the lcm of 13 and 117.
where,
13 is a positive integer,
117 is a positive integer,
117 is the lcm of 13 and 117,
{13} in {13, 3 x 3 x 13} is the common factors of 13 and 117,
{3 x 3} in {13, 3 x 3 x 13} are the uncommon factors of 13 and 117.
Use in Mathematics: LCM of 13 and 117
The below are some of the mathematical applications where lcm of 13 and 117 can be used:
- to find the least number which is exactly divisible by 13 and 117.
- to find the common denominator for two fractions having 13 and 117 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 13 and 117 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 117 seconds repeatedly. The answer is that all bells A and B toll together at 117 seconds for the first time, at 234 seconds for the second time, at 351 seconds for the third time and so on.
Important Notes: 13 and 117 lcm
The below are the important notes to be remembered while solving the lcm of 13 and 117:
- The common prime factors and the remaining prime factors of 13 and 117 should be multiplied to find the least common multiple of 13 and 117, when solving lcm by using prime factors method.
- The results of lcm of 13 and 117, and the lcm of 117 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 117?
The below solved example with step by step work shows how to find what is the lcm of 13 and 117 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 13 and 117?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 13
B = 117
What to be found:
find the lcm of 13 and 117
step 2 Find the prime factors of 13 and 117:
Prime factors of 13 = 13
Prime factors of 117 = 3 x 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 13 and 117:
{13} is the most repeated factor and {3 x 3} are the non-repeated factors of 13 and 117.
step 4 Find the product of repeated and non-repeated prime factors of 13 and 117:
= 13 x 3 x 3
= 117
lcm(13 and 117) = 117
Hence,
lcm of 13 and 117 is 117
This special division method is the easiest way to understand the entire calculation of what is the lcm of 13 and 117.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 13 and 117
What to be found:
lcm (13, 117) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
13 and 117
step 3 Choose the divisor which divides each or most of the given integers (13 and 117), 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 117 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 13 | 117 |
| 3 | 13 | 39 |
| 13 | 13 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 13 and 117:
= 3 x 3 x 13
= 117
LCM(13, 117) = 117
The least common multiple for two numbers 13 and 117 is 117