LCM of 218 and 222
24198 is the LCM of 218 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 218 and 222, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 218 and 222?
lcm (218 222) = (?)
218 => 2 x 109
222 => 2 x 3 x 37
= 2 x 109 x 3 x 37
= 24198
lcm (218 and 222) = 24198
24198 is the LCM of 218 and 222.
where,
218 is a positive integer,
222 is a positive integer,
24198 is the LCM of 218 and 222,
{2} in {2 x 109, 2 x 3 x 37} is the common factors of 218 and 222,
{109 x 3 x 37} in {2 x 109, 2 x 3 x 37} are the uncommon factors of 218 and 222.
Use in Mathematics: LCM of 218 and 222
The below are some of the mathematical applications where lcm of 218 and 222 can be used:
- to find the least number which is exactly divisible by 218 and 222.
- to find the common denominator for two fractions having 218 and 222 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 218 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 218 seconds and bell B tolls at 222 seconds repeatedly. The answer is that all bells A and B toll together at 24198 seconds for the first time, at 48396 seconds for the second time, at 72594 seconds for the third time and so on.
Important Notes: 218 and 222 lcm
The below are the important notes to be remembered while solving the lcm of 218 and 222:
- The common prime factors and the remaining prime factors of 218 and 222 should be multiplied to find the least common multiple of 218 and 222, when solving lcm by using prime factors method.
- The results of lcm of 218 and 222, and the lcm of 222 and 218 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 218 and 222?
The below solved example with step by step work shows how to find what is the lcm of 218 and 222 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 218 and 222?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 218
B = 222
What to be found:
find the lcm of 218 and 222
step 2 Find the prime factors of 218 and 222:
Prime factors of 218 = 2 x 109
Prime factors of 222 = 2 x 3 x 37
step 3 Identify the repeated and non-repeated prime factors of 218 and 222:
{2} is the most repeated factor and {109 x 3 x 37} are the non-repeated factors of 218 and 222.
step 4 Find the product of repeated and non-repeated prime factors of 218 and 222:
= 2 x 109 x 3 x 37
= 24198
lcm(218 and 222) = 24198
Hence,
lcm of 218 and 222 is 24198
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 218 and 222.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 218 and 222
What to be found:
lcm (218, 222) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
218 and 222
step 3 Choose the divisor which divides each or most of the given integers (218 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 218 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 | 218 | 222 |
| 3 | 109 | 111 |
| 37 | 109 | 37 |
| 109 | 109 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 218 and 222:
= 2 x 3 x 37 x 109
= 24198
LCM(218, 222) = 24198
The LCM of two numbers 218 and 222 is 24198