LCM of 27, 32 and 37
31968 is the LCM of 27, 32 and 37. 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 27, 32 and 37, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 27, 32 and 37?
lcm (27 32 37) = (?)
27 => 3 x 3 x 3
32 => 2 x 2 x 2 x 2 x 2
37 => 37
= 3 x 3 x 3 x 2 x 2 x 2 x 2 x 2 x 37
= 31968
lcm (27, 32 and 37) = 31968
The LCM of 27, 32 and 37 is 31968
where,
27 is a positive integer,
32 is a positive integer,
31968 is the LCM of 27, 32 and 37,
in {3 x 3 x 3, 2 x 2 x 2 x 2 x 2, 37} there is no repeated factors of 27, 32 and 37,
{3, 3, 3, 2, 2, 2, 2, 2, 37} in {3 x 3 x 3, 2 x 2 x 2 x 2 x 2, 37} are the the other remaining factors of 27, 32 and 37.
Use in Mathematics: LCM of 27, 32 and 37
The below are some of the mathematical applications where lcm of 27, 32 and 37 can be used:
- to find the least number which is exactly divisible by 27, 32 and 37.
- to find the common denominators for the fractions having 27, 32 and 37 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 27, 32 and 37 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 27 seconds, B tolls at 32 seconds and C tolls at 37 seconds repeatedly. The answer is that all bells A, B and C toll together at 31968 seconds for the first time, at 63936 seconds for the second time, at 95904 seconds for the third time and so on.
Important Notes: 27, 32 and 37 lcm
The below are the important notes to be remembered while solving the lcm of 27, 32 and 37:
- The repeated and non-repeated prime factors of 27, 32 and 37 should be multiplied to find the least common multiple of 27, 32 and 37, when solving lcm by using prime factors method.
- The results of lcm of 27, 32 and 37 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 LCM of 27, 32 and 37?
The below solved example with step by step work shows how to find what is the lcm of 27, 32 and 37 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 27, 32 and 37?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 27
B = 32
C = 37
What to be found:
Find lcm of 27, 32 and 37
step 2 Find the prime factors of 27, 32 and 37:
Prime factors of 27 = 3 x 3 x 3
Prime factors of 32 = 2 x 2 x 2 x 2 x 2
Prime factors of 37 = 37
step 3Identify the repeated and non-repeated prime factors of 27, 32 and 37:
Since there is no common factors between 27, 32 and 37, multiplying the given numbers directly provides the LCM of
27, 32 and 37.
= 27 x 32 x 37
= 31968
LCM(27, 32 and 37) = 31968
Hence,
The Least Common Multiple of 27, 32 and 37 is 31968
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 27, 32 and 37.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 27, 32 and 37
What to be found:
lcm (27, 32, 37) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
27, 32 and 37
step 3 Choose the divisor which divides each or most of the given integers (27, 32 and 37), 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 27, 32 and 37 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 27 | 32 | 37 |
| 2 | 27 | 16 | 37 |
| 2 | 27 | 8 | 37 |
| 2 | 27 | 4 | 37 |
| 2 | 27 | 2 | 37 |
| 3 | 27 | 1 | 37 |
| 3 | 9 | 1 | 37 |
| 3 | 3 | 1 | 37 |
| 37 | 1 | 1 | 37 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 27, 32 and 37:
= 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 37
= 31968
LCM(27, 32, 37) = 31968
The LCM of three numbers 27, 32 and 37 is 31968