13, 27 and 39 LCM
LCM of 13, 27 and 39 is equal to 351. The comprehensive work provides more insight of how to find what is the lcm of 13, 27 and 39 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, 27 and 39?
lcm (13 27 39) = (?)
13 => 13
27 => 3 x 3 x 3
39 => 3 x 13
= 3 x 13 x 3 x 3
= 351
lcm (13, 27 and 39) = 351
351 is the lcm of 13, 27 and 39.
where,
13 is a positive integer,
27 is a positive integer,
351 is the lcm of 13, 27 and 39,
{3, 13} in {13, 3 x 3 x 3, 3 x 13} are the most repeated factors of 13, 27 and 39,
{3, 3} in {13, 3 x 3 x 3, 3 x 13} are the the other remaining factors of 13, 27 and 39.
Use in Mathematics: LCM of 13, 27 and 39
The below are some of the mathematical applications where lcm of 13, 27 and 39 can be used:
- to find the least number which is exactly divisible by 13, 27 and 39.
- to find the common denominators for the fractions having 13, 27 and 39 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 13, 27 and 39 helps to find the exact time when three similar and recurring 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 all the bells A, B and C toll together, if bell A tolls at 13 seconds, B tolls at 27 seconds and C tolls at 39 seconds repeatedly. The answer is that all bells A, B and C toll together at 351 seconds for the first time, at 702 seconds for the second time, at 1053 seconds for the third time and so on.
Important Notes: 13, 27 and 39 lcm
The below are the important notes to be remembered while solving the lcm of 13, 27 and 39:
- The repeated and non-repeated prime factors of 13, 27 and 39 should be multiplied to find the least common multiple of 13, 27 and 39, when solving lcm by using prime factors method.
- The results of lcm of 13, 27 and 39 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 13, 27 and 39?
The below solved example with step by step work shows how to find what is the lcm of 13, 27 and 39 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 13, 27 and 39?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 13
B = 27
C = 39
What to be found:
find the lcm of 13, 27 and 39
step 2 Find the prime factors of 13, 27 and 39:
Prime factors of 13 = 13
Prime factors of 27 = 3 x 3 x 3
Prime factors of 39 = 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 13, 27 and 39:
{3, 13} are the most repeated factors and {3, 3} are the non-repeated factors of 13, 27 and 39.
step 4 Find the product of repeated and non-repeated prime factors of 13, 27 and 39:
= 3 x 13 x 3 x 3
= 351
lcm(20 and 30) = 351
Hence,
lcm of 13, 27 and 39 is 351
This special division method is the easiest way to understand the entire calculation of what is the lcm of 13, 27 and 39.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 13, 27 and 39
What to be found:
lcm (13, 27, 39) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
13, 27 and 39
step 3 Choose the divisor which divides each or most of the given integers (13, 27 and 39), 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, 27 and 39 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 13 | 27 | 39 |
| 3 | 13 | 9 | 13 |
| 3 | 13 | 3 | 13 |
| 13 | 13 | 1 | 13 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 13, 27 and 39:
= 3 x 3 x 3 x 13
= 351
LCM(13, 27, 39) = 351
The least common multiple for three numbers 13, 27 and 39 is 351