LCM of 111 and 198
7326 is the LCM of 111 and 198. 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 111 and 198, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 111 and 198?
lcm (111 198) = (?)
111 => 3 x 37
198 => 2 x 3 x 3 x 11
= 3 x 37 x 2 x 3 x 11
= 7326
lcm (111 and 198) = 7326
7326 is the LCM of 111 and 198.
where,
111 is a positive integer,
198 is a positive integer,
7326 is the LCM of 111 and 198,
{3} in {3 x 37, 2 x 3 x 3 x 11} is the common factors of 111 and 198,
{37 x 2 x 3 x 11} in {3 x 37, 2 x 3 x 3 x 11} are the uncommon factors of 111 and 198.
Use in Mathematics: LCM of 111 and 198
The below are some of the mathematical applications where lcm of 111 and 198 can be used:
- to find the least number which is exactly divisible by 111 and 198.
- to find the common denominator for two fractions having 111 and 198 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 111 and 198 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 111 seconds and bell B tolls at 198 seconds repeatedly. The answer is that all bells A and B toll together at 7326 seconds for the first time, at 14652 seconds for the second time, at 21978 seconds for the third time and so on.
Important Notes: 111 and 198 lcm
The below are the important notes to be remembered while solving the lcm of 111 and 198:
- The common prime factors and the remaining prime factors of 111 and 198 should be multiplied to find the least common multiple of 111 and 198, when solving lcm by using prime factors method.
- The results of lcm of 111 and 198, and the lcm of 198 and 111 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 111 and 198?
The below solved example with step by step work shows how to find what is the lcm of 111 and 198 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 111 and 198?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 111
B = 198
What to be found:
find the lcm of 111 and 198
step 2 Find the prime factors of 111 and 198:
Prime factors of 111 = 3 x 37
Prime factors of 198 = 2 x 3 x 3 x 11
step 3 Identify the repeated and non-repeated prime factors of 111 and 198:
{3} is the most repeated factor and {37 x 2 x 3 x 11} are the non-repeated factors of 111 and 198.
step 4 Find the product of repeated and non-repeated prime factors of 111 and 198:
= 3 x 37 x 2 x 3 x 11
= 7326
lcm(111 and 198) = 7326
Hence,
lcm of 111 and 198 is 7326
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 111 and 198.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 111 and 198
What to be found:
lcm (111, 198) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
111 and 198
step 3 Choose the divisor which divides each or most of the given integers (111 and 198), 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 111 and 198 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 111 | 198 |
| 3 | 111 | 99 |
| 3 | 37 | 33 |
| 11 | 37 | 11 |
| 37 | 37 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 111 and 198:
= 2 x 3 x 3 x 11 x 37
= 7326
LCM(111, 198) = 7326
The LCM of two numbers 111 and 198 is 7326