LCM of 12 and 27
108 is the LCM of 12 and 27. 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 12 and 27, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 12 and 27?
lcm (12 27) = (?)
12 => 2 x 2 x 3
27 => 3 x 3 x 3
= 3 x 2 x 2 x 3 x 3
= 108
lcm (12 and 27) = 108
108 is the LCM of 12 and 27.
where,
12 is a positive integer,
27 is a positive integer,
108 is the LCM of 12 and 27,
{3} in {2 x 2 x 3, 3 x 3 x 3} is the common factors of 12 and 27,
{2 x 2 x 3 x 3} in {2 x 2 x 3, 3 x 3 x 3} are the uncommon factors of 12 and 27.
Use in Mathematics: LCM of 12 and 27
The below are some of the mathematical applications where lcm of 12 and 27 can be used:
- to find the least number which is exactly divisible by 12 and 27.
- to find the common denominator for two fractions having 12 and 27 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 12 and 27 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 12 seconds and bell B tolls at 27 seconds repeatedly. The answer is that all bells A and B toll together at 108 seconds for the first time, at 216 seconds for the second time, at 324 seconds for the third time and so on.
Important Notes: 12 and 27 lcm
The below are the important notes to be remembered while solving the lcm of 12 and 27:
- The common prime factors and the remaining prime factors of 12 and 27 should be multiplied to find the least common multiple of 12 and 27, when solving lcm by using prime factors method.
- The results of lcm of 12 and 27, and the lcm of 27 and 12 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 12 and 27?
The below solved example with step by step work shows how to find what is the lcm of 12 and 27 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 12 and 27?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 12
B = 27
What to be found:
find the lcm of 12 and 27
step 2 Find the prime factors of 12 and 27:
Prime factors of 12 = 2 x 2 x 3
Prime factors of 27 = 3 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 12 and 27:
{3} is the most repeated factor and {2 x 2 x 3 x 3} are the non-repeated factors of 12 and 27.
step 4 Find the product of repeated and non-repeated prime factors of 12 and 27:
= 3 x 2 x 2 x 3 x 3
= 108
lcm(12 and 27) = 108
Hence,
lcm of 12 and 27 is 108
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 12 and 27.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 12 and 27
What to be found:
lcm (12, 27) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
12 and 27
step 3 Choose the divisor which divides each or most of the given integers (12 and 27), 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 12 and 27 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 12 | 27 |
| 2 | 6 | 27 |
| 3 | 3 | 27 |
| 3 | 1 | 9 |
| 3 | 1 | 3 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 12 and 27:
= 2 x 2 x 3 x 3 x 3
= 108
LCM(12, 27) = 108
The LCM of two numbers 12 and 27 is 108