165 and 187 LCM
LCM of 165 and 187 is equal to 2805. The comprehensive work provides more insight of how to find what is the lcm of 165 and 187 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 165 and 187?
lcm (165 187) = (?)
165 => 3 x 5 x 11
187 => 11 x 17
= 11 x 3 x 5 x 17
= 2805
lcm (165 and 187) = 2805
2805 is the lcm of 165 and 187.
where,
165 is a positive integer,
187 is a positive integer,
2805 is the lcm of 165 and 187,
{11} in {3 x 5 x 11, 11 x 17} is the common factors of 165 and 187,
{3 x 5 x 17} in {3 x 5 x 11, 11 x 17} are the uncommon factors of 165 and 187.
Use in Mathematics: LCM of 165 and 187
The below are some of the mathematical applications where lcm of 165 and 187 can be used:
- to find the least number which is exactly divisible by 165 and 187.
- to find the common denominator for two fractions having 165 and 187 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 165 and 187 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 165 seconds and bell B tolls at 187 seconds repeatedly. The answer is that all bells A and B toll together at 2805 seconds for the first time, at 5610 seconds for the second time, at 8415 seconds for the third time and so on.
Important Notes: 165 and 187 lcm
The below are the important notes to be remembered while solving the lcm of 165 and 187:
- The common prime factors and the remaining prime factors of 165 and 187 should be multiplied to find the least common multiple of 165 and 187, when solving lcm by using prime factors method.
- The results of lcm of 165 and 187, and the lcm of 187 and 165 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 165 and 187?
The below solved example with step by step work shows how to find what is the lcm of 165 and 187 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 165 and 187?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 165
B = 187
What to be found:
find the lcm of 165 and 187
step 2 Find the prime factors of 165 and 187:
Prime factors of 165 = 3 x 5 x 11
Prime factors of 187 = 11 x 17
step 3 Identify the repeated and non-repeated prime factors of 165 and 187:
{11} is the most repeated factor and {3 x 5 x 17} are the non-repeated factors of 165 and 187.
step 4 Find the product of repeated and non-repeated prime factors of 165 and 187:
= 11 x 3 x 5 x 17
= 2805
lcm(165 and 187) = 2805
Hence,
lcm of 165 and 187 is 2805
This special division method is the easiest way to understand the entire calculation of what is the lcm of 165 and 187.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 165 and 187
What to be found:
lcm (165, 187) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
165 and 187
step 3 Choose the divisor which divides each or most of the given integers (165 and 187), 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 165 and 187 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 165 | 187 |
| 5 | 55 | 187 |
| 11 | 11 | 187 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 165 and 187:
= 3 x 5 x 11 x 17
= 2805
LCM(165, 187) = 2805
The least common multiple for two numbers 165 and 187 is 2805