LCM of 186 and 267
16554 is the LCM of 186 and 267. 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 186 and 267, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 186 and 267?
lcm (186 267) = (?)
186 => 2 x 3 x 31
267 => 3 x 89
= 3 x 2 x 31 x 89
= 16554
lcm (186 and 267) = 16554
16554 is the LCM of 186 and 267.
where,
186 is a positive integer,
267 is a positive integer,
16554 is the LCM of 186 and 267,
{3} in {2 x 3 x 31, 3 x 89} is the common factors of 186 and 267,
{2 x 31 x 89} in {2 x 3 x 31, 3 x 89} are the uncommon factors of 186 and 267.
Use in Mathematics: LCM of 186 and 267
The below are some of the mathematical applications where lcm of 186 and 267 can be used:
- to find the least number which is exactly divisible by 186 and 267.
- to find the common denominator for two fractions having 186 and 267 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 186 and 267 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 186 seconds and bell B tolls at 267 seconds repeatedly. The answer is that all bells A and B toll together at 16554 seconds for the first time, at 33108 seconds for the second time, at 49662 seconds for the third time and so on.
Important Notes: 186 and 267 lcm
The below are the important notes to be remembered while solving the lcm of 186 and 267:
- The common prime factors and the remaining prime factors of 186 and 267 should be multiplied to find the least common multiple of 186 and 267, when solving lcm by using prime factors method.
- The results of lcm of 186 and 267, and the lcm of 267 and 186 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 186 and 267?
The below solved example with step by step work shows how to find what is the lcm of 186 and 267 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 186 and 267?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 186
B = 267
What to be found:
find the lcm of 186 and 267
step 2 Find the prime factors of 186 and 267:
Prime factors of 186 = 2 x 3 x 31
Prime factors of 267 = 3 x 89
step 3 Identify the repeated and non-repeated prime factors of 186 and 267:
{3} is the most repeated factor and {2 x 31 x 89} are the non-repeated factors of 186 and 267.
step 4 Find the product of repeated and non-repeated prime factors of 186 and 267:
= 3 x 2 x 31 x 89
= 16554
lcm(186 and 267) = 16554
Hence,
lcm of 186 and 267 is 16554
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 186 and 267.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 186 and 267
What to be found:
lcm (186, 267) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
186 and 267
step 3 Choose the divisor which divides each or most of the given integers (186 and 267), 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 186 and 267 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 186 | 267 |
| 3 | 93 | 267 |
| 31 | 31 | 89 |
| 89 | 1 | 89 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 186 and 267:
= 2 x 3 x 31 x 89
= 16554
LCM(186, 267) = 16554
The LCM of two numbers 186 and 267 is 16554