LCM of 198 and 261
5742 is the LCM of 198 and 261. 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 198 and 261, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 198 and 261?
lcm (198 261) = (?)
198 => 2 x 3 x 3 x 11
261 => 3 x 3 x 29
= 3 x 3 x 2 x 11 x 29
= 5742
lcm (198 and 261) = 5742
5742 is the LCM of 198 and 261.
where,
198 is a positive integer,
261 is a positive integer,
5742 is the LCM of 198 and 261,
{3 x 3} in {2 x 3 x 3 x 11, 3 x 3 x 29} are the common factors of 198 and 261,
{2 x 11 x 29} in {2 x 3 x 3 x 11, 3 x 3 x 29} are the uncommon factors of 198 and 261.
Use in Mathematics: LCM of 198 and 261
The below are some of the mathematical applications where lcm of 198 and 261 can be used:
- to find the least number which is exactly divisible by 198 and 261.
- to find the common denominator for two fractions having 198 and 261 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 198 and 261 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 198 seconds and bell B tolls at 261 seconds repeatedly. The answer is that all bells A and B toll together at 5742 seconds for the first time, at 11484 seconds for the second time, at 17226 seconds for the third time and so on.
Important Notes: 198 and 261 lcm
The below are the important notes to be remembered while solving the lcm of 198 and 261:
- The common prime factors and the remaining prime factors of 198 and 261 should be multiplied to find the least common multiple of 198 and 261, when solving lcm by using prime factors method.
- The results of lcm of 198 and 261, and the lcm of 261 and 198 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 198 and 261?
The below solved example with step by step work shows how to find what is the lcm of 198 and 261 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 198 and 261?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 198
B = 261
What to be found:
find the lcm of 198 and 261
step 2 Find the prime factors of 198 and 261:
Prime factors of 198 = 2 x 3 x 3 x 11
Prime factors of 261 = 3 x 3 x 29
step 3 Identify the repeated and non-repeated prime factors of 198 and 261:
{3, 3} are the most repeated factors and {2 x 11 x 29} are the non-repeated factors of 198 and 261.
step 4 Find the product of repeated and non-repeated prime factors of 198 and 261:
= 3 x 3 x 2 x 11 x 29
= 5742
lcm(198 and 261) = 5742
Hence,
lcm of 198 and 261 is 5742
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 198 and 261.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 198 and 261
What to be found:
lcm (198, 261) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
198 and 261
step 3 Choose the divisor which divides each or most of the given integers (198 and 261), 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 198 and 261 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 198 | 261 |
| 3 | 99 | 261 |
| 3 | 33 | 87 |
| 11 | 11 | 29 |
| 29 | 1 | 29 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 198 and 261:
= 2 x 3 x 3 x 11 x 29
= 5742
LCM(198, 261) = 5742
The LCM of two numbers 198 and 261 is 5742