LCM of 57 and 111
2109 is the LCM of 57 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 57 and 111, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 57 and 111?
lcm (57 111) = (?)
57 => 3 x 19
111 => 3 x 37
= 3 x 19 x 37
= 2109
lcm (57 and 111) = 2109
2109 is the LCM of 57 and 111.
where,
57 is a positive integer,
111 is a positive integer,
2109 is the LCM of 57 and 111,
{3} in {3 x 19, 3 x 37} is the common factors of 57 and 111,
{19 x 37} in {3 x 19, 3 x 37} are the uncommon factors of 57 and 111.
Use in Mathematics: LCM of 57 and 111
The below are some of the mathematical applications where lcm of 57 and 111 can be used:
- to find the least number which is exactly divisible by 57 and 111.
- to find the common denominator for two fractions having 57 and 111 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 57 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 57 seconds and bell B tolls at 111 seconds repeatedly. The answer is that all bells A and B toll together at 2109 seconds for the first time, at 4218 seconds for the second time, at 6327 seconds for the third time and so on.
Important Notes: 57 and 111 lcm
The below are the important notes to be remembered while solving the lcm of 57 and 111:
- The common prime factors and the remaining prime factors of 57 and 111 should be multiplied to find the least common multiple of 57 and 111, when solving lcm by using prime factors method.
- The results of lcm of 57 and 111, and the lcm of 111 and 57 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 57 and 111?
The below solved example with step by step work shows how to find what is the lcm of 57 and 111 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 57 and 111?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 57
B = 111
What to be found:
find the lcm of 57 and 111
step 2 Find the prime factors of 57 and 111:
Prime factors of 57 = 3 x 19
Prime factors of 111 = 3 x 37
step 3 Identify the repeated and non-repeated prime factors of 57 and 111:
{3} is the most repeated factor and {19 x 37} are the non-repeated factors of 57 and 111.
step 4 Find the product of repeated and non-repeated prime factors of 57 and 111:
= 3 x 19 x 37
= 2109
lcm(57 and 111) = 2109
Hence,
lcm of 57 and 111 is 2109
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 57 and 111.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 57 and 111
What to be found:
lcm (57, 111) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
57 and 111
step 3 Choose the divisor which divides each or most of the given integers (57 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 57 and 111 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 57 | 111 |
| 19 | 19 | 37 |
| 37 | 1 | 37 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 57 and 111:
= 3 x 19 x 37
= 2109
LCM(57, 111) = 2109
The LCM of two numbers 57 and 111 is 2109