LCM of 165 and 306
16830 is the LCM of 165 and 306. 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 165 and 306, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 165 and 306?
lcm (165 306) = (?)
165 => 3 x 5 x 11
306 => 2 x 3 x 3 x 17
= 3 x 5 x 11 x 2 x 3 x 17
= 16830
lcm (165 and 306) = 16830
16830 is the LCM of 165 and 306.
where,
165 is a positive integer,
306 is a positive integer,
16830 is the LCM of 165 and 306,
{3} in {3 x 5 x 11, 2 x 3 x 3 x 17} is the common factors of 165 and 306,
{5 x 11 x 2 x 3 x 17} in {3 x 5 x 11, 2 x 3 x 3 x 17} are the uncommon factors of 165 and 306.
Use in Mathematics: LCM of 165 and 306
The below are some of the mathematical applications where lcm of 165 and 306 can be used:
- to find the least number which is exactly divisible by 165 and 306.
- to find the common denominator for two fractions having 165 and 306 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 165 and 306 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 306 seconds repeatedly. The answer is that all bells A and B toll together at 16830 seconds for the first time, at 33660 seconds for the second time, at 50490 seconds for the third time and so on.
Important Notes: 165 and 306 lcm
The below are the important notes to be remembered while solving the lcm of 165 and 306:
- The common prime factors and the remaining prime factors of 165 and 306 should be multiplied to find the least common multiple of 165 and 306, when solving lcm by using prime factors method.
- The results of lcm of 165 and 306, and the lcm of 306 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 306?
The below solved example with step by step work shows how to find what is the lcm of 165 and 306 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 165 and 306?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 165
B = 306
What to be found:
find the lcm of 165 and 306
step 2 Find the prime factors of 165 and 306:
Prime factors of 165 = 3 x 5 x 11
Prime factors of 306 = 2 x 3 x 3 x 17
step 3 Identify the repeated and non-repeated prime factors of 165 and 306:
{3} is the most repeated factor and {5 x 11 x 2 x 3 x 17} are the non-repeated factors of 165 and 306.
step 4 Find the product of repeated and non-repeated prime factors of 165 and 306:
= 3 x 5 x 11 x 2 x 3 x 17
= 16830
lcm(165 and 306) = 16830
Hence,
lcm of 165 and 306 is 16830
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 165 and 306.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 165 and 306
What to be found:
lcm (165, 306) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
165 and 306
step 3 Choose the divisor which divides each or most of the given integers (165 and 306), 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 306 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 165 | 306 |
| 3 | 165 | 153 |
| 3 | 55 | 51 |
| 5 | 55 | 17 |
| 11 | 11 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 165 and 306:
= 2 x 3 x 3 x 5 x 11 x 17
= 16830
LCM(165, 306) = 16830
The LCM of two numbers 165 and 306 is 16830