LCM of 214 and 271
57994 is the LCM of 214 and 271. 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 214 and 271, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 214 and 271?
lcm (214 271) = (?)
214 => 2 x 107
271 => 271
= 2 x 107 x 271
= 57994
lcm (214 and 271) = 57994
57994 is the LCM of 214 and 271.
where,
214 is a positive integer,
271 is a positive integer,
57994 is the LCM of 214 and 271,
There is no common factors of 214 and 271 in {2 x 107, 271},
{2 x 107 x 271} in {2 x 107, 271} are the uncommon factors of 214 and 271.
Use in Mathematics: LCM of 214 and 271
The below are some of the mathematical applications where lcm of 214 and 271 can be used:
- to find the least number which is exactly divisible by 214 and 271.
- to find the common denominator for two fractions having 214 and 271 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 214 and 271 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 214 seconds and bell B tolls at 271 seconds repeatedly. The answer is that all bells A and B toll together at 57994 seconds for the first time, at 115988 seconds for the second time, at 173982 seconds for the third time and so on.
Important Notes: 214 and 271 lcm
The below are the important notes to be remembered while solving the lcm of 214 and 271:
- The common prime factors and the remaining prime factors of 214 and 271 should be multiplied to find the least common multiple of 214 and 271, when solving lcm by using prime factors method.
- The results of lcm of 214 and 271, and the lcm of 271 and 214 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 214 and 271?
The below solved example with step by step work shows how to find what is the lcm of 214 and 271 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 214 and 271?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 214
B = 271
What to be found:
find the lcm of 214 and 271
step 2 Find the prime factors of 214 and 271:
Prime factors of 214 = 2 x 107
Prime factors of 271 = 271
step 3Identify the repeated and non-repeated prime factors of 214 and 271:
Since there is no common factors between 214 and 271, multiplying the given numbers directly provides the LCM of
214 and 271.
= 214 x 271
= 57994
lcm(214 and 271) = 57994
Hence,
lcm of 214 and 271 is 57994
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 214 and 271.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 214 and 271
What to be found:
lcm (214, 271) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
214 and 271
step 3 Choose the divisor which divides each or most of the given integers (214 and 271), 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 214 and 271 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 214 | 271 |
| 107 | 107 | 271 |
| 271 | 1 | 271 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 214 and 271:
= 2 x 107 x 271
= 57994
LCM(214, 271) = 57994
The LCM of two numbers 214 and 271 is 57994