LCM of 111 and 318
11766 is the LCM of 111 and 318. 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 318, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 111 and 318?
lcm (111 318) = (?)
111 => 3 x 37
318 => 2 x 3 x 53
= 3 x 37 x 2 x 53
= 11766
lcm (111 and 318) = 11766
11766 is the LCM of 111 and 318.
where,
111 is a positive integer,
318 is a positive integer,
11766 is the LCM of 111 and 318,
{3} in {3 x 37, 2 x 3 x 53} is the common factors of 111 and 318,
{37 x 2 x 53} in {3 x 37, 2 x 3 x 53} are the uncommon factors of 111 and 318.
Use in Mathematics: LCM of 111 and 318
The below are some of the mathematical applications where lcm of 111 and 318 can be used:
- to find the least number which is exactly divisible by 111 and 318.
- to find the common denominator for two fractions having 111 and 318 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 111 and 318 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 318 seconds repeatedly. The answer is that all bells A and B toll together at 11766 seconds for the first time, at 23532 seconds for the second time, at 35298 seconds for the third time and so on.
Important Notes: 111 and 318 lcm
The below are the important notes to be remembered while solving the lcm of 111 and 318:
- The common prime factors and the remaining prime factors of 111 and 318 should be multiplied to find the least common multiple of 111 and 318, when solving lcm by using prime factors method.
- The results of lcm of 111 and 318, and the lcm of 318 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 318?
The below solved example with step by step work shows how to find what is the lcm of 111 and 318 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 111 and 318?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 111
B = 318
What to be found:
find the lcm of 111 and 318
step 2 Find the prime factors of 111 and 318:
Prime factors of 111 = 3 x 37
Prime factors of 318 = 2 x 3 x 53
step 3 Identify the repeated and non-repeated prime factors of 111 and 318:
{3} is the most repeated factor and {37 x 2 x 53} are the non-repeated factors of 111 and 318.
step 4 Find the product of repeated and non-repeated prime factors of 111 and 318:
= 3 x 37 x 2 x 53
= 11766
lcm(111 and 318) = 11766
Hence,
lcm of 111 and 318 is 11766
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 111 and 318.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 111 and 318
What to be found:
lcm (111, 318) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
111 and 318
step 3 Choose the divisor which divides each or most of the given integers (111 and 318), 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 318 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 111 | 318 |
| 3 | 111 | 159 |
| 37 | 37 | 53 |
| 53 | 1 | 53 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 111 and 318:
= 2 x 3 x 37 x 53
= 11766
LCM(111, 318) = 11766
The LCM of two numbers 111 and 318 is 11766