LCM of 114 and 201
7638 is the LCM of 114 and 201. 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 201, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 114 and 201?
lcm (114 201) = (?)
114 => 2 x 3 x 19
201 => 3 x 67
= 3 x 2 x 19 x 67
= 7638
lcm (114 and 201) = 7638
7638 is the LCM of 114 and 201.
where,
114 is a positive integer,
201 is a positive integer,
7638 is the LCM of 114 and 201,
{3} in {2 x 3 x 19, 3 x 67} is the common factors of 114 and 201,
{2 x 19 x 67} in {2 x 3 x 19, 3 x 67} are the uncommon factors of 114 and 201.
Use in Mathematics: LCM of 114 and 201
The below are some of the mathematical applications where lcm of 114 and 201 can be used:
- to find the least number which is exactly divisible by 114 and 201.
- to find the common denominator for two fractions having 114 and 201 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 114 and 201 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 201 seconds repeatedly. The answer is that all bells A and B toll together at 7638 seconds for the first time, at 15276 seconds for the second time, at 22914 seconds for the third time and so on.
Important Notes: 114 and 201 lcm
The below are the important notes to be remembered while solving the lcm of 114 and 201:
- The common prime factors and the remaining prime factors of 114 and 201 should be multiplied to find the least common multiple of 114 and 201, when solving lcm by using prime factors method.
- The results of lcm of 114 and 201, and the lcm of 201 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 201?
The below solved example with step by step work shows how to find what is the lcm of 114 and 201 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 114 and 201?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 114
B = 201
What to be found:
find the lcm of 114 and 201
step 2 Find the prime factors of 114 and 201:
Prime factors of 114 = 2 x 3 x 19
Prime factors of 201 = 3 x 67
step 3 Identify the repeated and non-repeated prime factors of 114 and 201:
{3} is the most repeated factor and {2 x 19 x 67} are the non-repeated factors of 114 and 201.
step 4 Find the product of repeated and non-repeated prime factors of 114 and 201:
= 3 x 2 x 19 x 67
= 7638
lcm(114 and 201) = 7638
Hence,
lcm of 114 and 201 is 7638
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 114 and 201.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 114 and 201
What to be found:
lcm (114, 201) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
114 and 201
step 3 Choose the divisor which divides each or most of the given integers (114 and 201), 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 201 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 114 | 201 |
| 3 | 57 | 201 |
| 19 | 19 | 67 |
| 67 | 1 | 67 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 114 and 201:
= 2 x 3 x 19 x 67
= 7638
LCM(114, 201) = 7638
The LCM of two numbers 114 and 201 is 7638