LCM of 108 and 111
3996 is the LCM of 108 and 111. 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 108 and 111, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 108 and 111?
lcm (108 111) = (?)
108 => 2 x 2 x 3 x 3 x 3
111 => 3 x 37
= 3 x 2 x 2 x 3 x 3 x 37
= 3996
lcm (108 and 111) = 3996
3996 is the LCM of 108 and 111.
where,
108 is a positive integer,
111 is a positive integer,
3996 is the LCM of 108 and 111,
{3} in {2 x 2 x 3 x 3 x 3, 3 x 37} is the common factors of 108 and 111,
{2 x 2 x 3 x 3 x 37} in {2 x 2 x 3 x 3 x 3, 3 x 37} are the uncommon factors of 108 and 111.
Use in Mathematics: LCM of 108 and 111
The below are some of the mathematical applications where lcm of 108 and 111 can be used:
- to find the least number which is exactly divisible by 108 and 111.
- to find the common denominator for two fractions having 108 and 111 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 108 and 111 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 108 seconds and bell B tolls at 111 seconds repeatedly. The answer is that all bells A and B toll together at 3996 seconds for the first time, at 7992 seconds for the second time, at 11988 seconds for the third time and so on.
Important Notes: 108 and 111 lcm
The below are the important notes to be remembered while solving the lcm of 108 and 111:
- The common prime factors and the remaining prime factors of 108 and 111 should be multiplied to find the least common multiple of 108 and 111, when solving lcm by using prime factors method.
- The results of lcm of 108 and 111, and the lcm of 111 and 108 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 108 and 111?
The below solved example with step by step work shows how to find what is the lcm of 108 and 111 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 108 and 111?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 108
B = 111
What to be found:
find the lcm of 108 and 111
step 2 Find the prime factors of 108 and 111:
Prime factors of 108 = 2 x 2 x 3 x 3 x 3
Prime factors of 111 = 3 x 37
step 3 Identify the repeated and non-repeated prime factors of 108 and 111:
{3} is the most repeated factor and {2 x 2 x 3 x 3 x 37} are the non-repeated factors of 108 and 111.
step 4 Find the product of repeated and non-repeated prime factors of 108 and 111:
= 3 x 2 x 2 x 3 x 3 x 37
= 3996
lcm(108 and 111) = 3996
Hence,
lcm of 108 and 111 is 3996
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 108 and 111.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 108 and 111
What to be found:
lcm (108, 111) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
108 and 111
step 3 Choose the divisor which divides each or most of the given integers (108 and 111), 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 108 and 111 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 108 | 111 |
| 2 | 54 | 111 |
| 3 | 27 | 111 |
| 3 | 9 | 37 |
| 3 | 3 | 37 |
| 37 | 1 | 37 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 108 and 111:
= 2 x 2 x 3 x 3 x 3 x 37
= 3996
LCM(108, 111) = 3996
The LCM of two numbers 108 and 111 is 3996