LCM of 214 and 254
27178 is the LCM of 214 and 254. 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 254, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 214 and 254?
lcm (214 254) = (?)
214 => 2 x 107
254 => 2 x 127
= 2 x 107 x 127
= 27178
lcm (214 and 254) = 27178
27178 is the LCM of 214 and 254.
where,
214 is a positive integer,
254 is a positive integer,
27178 is the LCM of 214 and 254,
{2} in {2 x 107, 2 x 127} is the common factors of 214 and 254,
{107 x 127} in {2 x 107, 2 x 127} are the uncommon factors of 214 and 254.
Use in Mathematics: LCM of 214 and 254
The below are some of the mathematical applications where lcm of 214 and 254 can be used:
- to find the least number which is exactly divisible by 214 and 254.
- to find the common denominator for two fractions having 214 and 254 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 214 and 254 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 254 seconds repeatedly. The answer is that all bells A and B toll together at 27178 seconds for the first time, at 54356 seconds for the second time, at 81534 seconds for the third time and so on.
Important Notes: 214 and 254 lcm
The below are the important notes to be remembered while solving the lcm of 214 and 254:
- The common prime factors and the remaining prime factors of 214 and 254 should be multiplied to find the least common multiple of 214 and 254, when solving lcm by using prime factors method.
- The results of lcm of 214 and 254, and the lcm of 254 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 254?
The below solved example with step by step work shows how to find what is the lcm of 214 and 254 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 214 and 254?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 214
B = 254
What to be found:
find the lcm of 214 and 254
step 2 Find the prime factors of 214 and 254:
Prime factors of 214 = 2 x 107
Prime factors of 254 = 2 x 127
step 3 Identify the repeated and non-repeated prime factors of 214 and 254:
{2} is the most repeated factor and {107 x 127} are the non-repeated factors of 214 and 254.
step 4 Find the product of repeated and non-repeated prime factors of 214 and 254:
= 2 x 107 x 127
= 27178
lcm(214 and 254) = 27178
Hence,
lcm of 214 and 254 is 27178
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 214 and 254.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 214 and 254
What to be found:
lcm (214, 254) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
214 and 254
step 3 Choose the divisor which divides each or most of the given integers (214 and 254), 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 254 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 214 | 254 |
| 107 | 107 | 127 |
| 127 | 1 | 127 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 214 and 254:
= 2 x 107 x 127
= 27178
LCM(214, 254) = 27178
The LCM of two numbers 214 and 254 is 27178