LCM of 214 and 222
23754 is the LCM of 214 and 222. 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 222, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 214 and 222?
lcm (214 222) = (?)
214 => 2 x 107
222 => 2 x 3 x 37
= 2 x 107 x 3 x 37
= 23754
lcm (214 and 222) = 23754
23754 is the LCM of 214 and 222.
where,
214 is a positive integer,
222 is a positive integer,
23754 is the LCM of 214 and 222,
{2} in {2 x 107, 2 x 3 x 37} is the common factors of 214 and 222,
{107 x 3 x 37} in {2 x 107, 2 x 3 x 37} are the uncommon factors of 214 and 222.
Use in Mathematics: LCM of 214 and 222
The below are some of the mathematical applications where lcm of 214 and 222 can be used:
- to find the least number which is exactly divisible by 214 and 222.
- to find the common denominator for two fractions having 214 and 222 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 214 and 222 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 222 seconds repeatedly. The answer is that all bells A and B toll together at 23754 seconds for the first time, at 47508 seconds for the second time, at 71262 seconds for the third time and so on.
Important Notes: 214 and 222 lcm
The below are the important notes to be remembered while solving the lcm of 214 and 222:
- The common prime factors and the remaining prime factors of 214 and 222 should be multiplied to find the least common multiple of 214 and 222, when solving lcm by using prime factors method.
- The results of lcm of 214 and 222, and the lcm of 222 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 222?
The below solved example with step by step work shows how to find what is the lcm of 214 and 222 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 214 and 222?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 214
B = 222
What to be found:
find the lcm of 214 and 222
step 2 Find the prime factors of 214 and 222:
Prime factors of 214 = 2 x 107
Prime factors of 222 = 2 x 3 x 37
step 3 Identify the repeated and non-repeated prime factors of 214 and 222:
{2} is the most repeated factor and {107 x 3 x 37} are the non-repeated factors of 214 and 222.
step 4 Find the product of repeated and non-repeated prime factors of 214 and 222:
= 2 x 107 x 3 x 37
= 23754
lcm(214 and 222) = 23754
Hence,
lcm of 214 and 222 is 23754
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 214 and 222.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 214 and 222
What to be found:
lcm (214, 222) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
214 and 222
step 3 Choose the divisor which divides each or most of the given integers (214 and 222), 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 222 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 214 | 222 |
| 3 | 107 | 111 |
| 37 | 107 | 37 |
| 107 | 107 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 214 and 222:
= 2 x 3 x 37 x 107
= 23754
LCM(214, 222) = 23754
The LCM of two numbers 214 and 222 is 23754