LCM of 114 and 218
12426 is the LCM of 114 and 218. 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 114 and 218, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 114 and 218?
lcm (114 218) = (?)
114 => 2 x 3 x 19
218 => 2 x 109
= 2 x 3 x 19 x 109
= 12426
lcm (114 and 218) = 12426
12426 is the LCM of 114 and 218.
where,
114 is a positive integer,
218 is a positive integer,
12426 is the LCM of 114 and 218,
{2} in {2 x 3 x 19, 2 x 109} is the common factors of 114 and 218,
{3 x 19 x 109} in {2 x 3 x 19, 2 x 109} are the uncommon factors of 114 and 218.
Use in Mathematics: LCM of 114 and 218
The below are some of the mathematical applications where lcm of 114 and 218 can be used:
- to find the least number which is exactly divisible by 114 and 218.
- to find the common denominator for two fractions having 114 and 218 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 114 and 218 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 114 seconds and bell B tolls at 218 seconds repeatedly. The answer is that all bells A and B toll together at 12426 seconds for the first time, at 24852 seconds for the second time, at 37278 seconds for the third time and so on.
Important Notes: 114 and 218 lcm
The below are the important notes to be remembered while solving the lcm of 114 and 218:
- The common prime factors and the remaining prime factors of 114 and 218 should be multiplied to find the least common multiple of 114 and 218, when solving lcm by using prime factors method.
- The results of lcm of 114 and 218, and the lcm of 218 and 114 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 114 and 218?
The below solved example with step by step work shows how to find what is the lcm of 114 and 218 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 114 and 218?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 114
B = 218
What to be found:
find the lcm of 114 and 218
step 2 Find the prime factors of 114 and 218:
Prime factors of 114 = 2 x 3 x 19
Prime factors of 218 = 2 x 109
step 3 Identify the repeated and non-repeated prime factors of 114 and 218:
{2} is the most repeated factor and {3 x 19 x 109} are the non-repeated factors of 114 and 218.
step 4 Find the product of repeated and non-repeated prime factors of 114 and 218:
= 2 x 3 x 19 x 109
= 12426
lcm(114 and 218) = 12426
Hence,
lcm of 114 and 218 is 12426
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 114 and 218.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 114 and 218
What to be found:
lcm (114, 218) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
114 and 218
step 3 Choose the divisor which divides each or most of the given integers (114 and 218), 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 114 and 218 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 114 | 218 |
| 3 | 57 | 109 |
| 19 | 19 | 109 |
| 109 | 1 | 109 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 114 and 218:
= 2 x 3 x 19 x 109
= 12426
LCM(114, 218) = 12426
The LCM of two numbers 114 and 218 is 12426