LCM of 111 and 128
14208 is the LCM of 111 and 128. 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 128, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 111 and 128?
lcm (111 128) = (?)
111 => 3 x 37
128 => 2 x 2 x 2 x 2 x 2 x 2 x 2
= 3 x 37 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 14208
lcm (111 and 128) = 14208
14208 is the LCM of 111 and 128.
where,
111 is a positive integer,
128 is a positive integer,
14208 is the LCM of 111 and 128,
There is no common factors of 111 and 128 in {3 x 37, 2 x 2 x 2 x 2 x 2 x 2 x 2},
{3 x 37 x 2 x 2 x 2 x 2 x 2 x 2 x 2} in {3 x 37, 2 x 2 x 2 x 2 x 2 x 2 x 2} are the uncommon factors of 111 and 128.
Use in Mathematics: LCM of 111 and 128
The below are some of the mathematical applications where lcm of 111 and 128 can be used:
- to find the least number which is exactly divisible by 111 and 128.
- to find the common denominator for two fractions having 111 and 128 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 111 and 128 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 128 seconds repeatedly. The answer is that all bells A and B toll together at 14208 seconds for the first time, at 28416 seconds for the second time, at 42624 seconds for the third time and so on.
Important Notes: 111 and 128 lcm
The below are the important notes to be remembered while solving the lcm of 111 and 128:
- The common prime factors and the remaining prime factors of 111 and 128 should be multiplied to find the least common multiple of 111 and 128, when solving lcm by using prime factors method.
- The results of lcm of 111 and 128, and the lcm of 128 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 128?
The below solved example with step by step work shows how to find what is the lcm of 111 and 128 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 111 and 128?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 111
B = 128
What to be found:
find the lcm of 111 and 128
step 2 Find the prime factors of 111 and 128:
Prime factors of 111 = 3 x 37
Prime factors of 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
step 3Identify the repeated and non-repeated prime factors of 111 and 128:
Since there is no common factors between 111 and 128, multiplying the given numbers directly provides the LCM of
111 and 128.
= 111 x 128
= 14208
lcm(111 and 128) = 14208
Hence,
lcm of 111 and 128 is 14208
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 111 and 128.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 111 and 128
What to be found:
lcm (111, 128) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
111 and 128
step 3 Choose the divisor which divides each or most of the given integers (111 and 128), 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 128 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 111 | 128 |
| 2 | 111 | 64 |
| 2 | 111 | 32 |
| 2 | 111 | 16 |
| 2 | 111 | 8 |
| 2 | 111 | 4 |
| 2 | 111 | 2 |
| 3 | 111 | 1 |
| 37 | 37 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 111 and 128:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 37
= 14208
LCM(111, 128) = 14208
The LCM of two numbers 111 and 128 is 14208