LCM of 165 and 333
18315 is the LCM of 165 and 333. 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 333, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 165 and 333?
lcm (165 333) = (?)
165 => 3 x 5 x 11
333 => 3 x 3 x 37
= 3 x 5 x 11 x 3 x 37
= 18315
lcm (165 and 333) = 18315
18315 is the LCM of 165 and 333.
where,
165 is a positive integer,
333 is a positive integer,
18315 is the LCM of 165 and 333,
{3} in {3 x 5 x 11, 3 x 3 x 37} is the common factors of 165 and 333,
{5 x 11 x 3 x 37} in {3 x 5 x 11, 3 x 3 x 37} are the uncommon factors of 165 and 333.
Use in Mathematics: LCM of 165 and 333
The below are some of the mathematical applications where lcm of 165 and 333 can be used:
- to find the least number which is exactly divisible by 165 and 333.
- to find the common denominator for two fractions having 165 and 333 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 165 and 333 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 333 seconds repeatedly. The answer is that all bells A and B toll together at 18315 seconds for the first time, at 36630 seconds for the second time, at 54945 seconds for the third time and so on.
Important Notes: 165 and 333 lcm
The below are the important notes to be remembered while solving the lcm of 165 and 333:
- The common prime factors and the remaining prime factors of 165 and 333 should be multiplied to find the least common multiple of 165 and 333, when solving lcm by using prime factors method.
- The results of lcm of 165 and 333, and the lcm of 333 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 333?
The below solved example with step by step work shows how to find what is the lcm of 165 and 333 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 165 and 333?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 165
B = 333
What to be found:
find the lcm of 165 and 333
step 2 Find the prime factors of 165 and 333:
Prime factors of 165 = 3 x 5 x 11
Prime factors of 333 = 3 x 3 x 37
step 3 Identify the repeated and non-repeated prime factors of 165 and 333:
{3} is the most repeated factor and {5 x 11 x 3 x 37} are the non-repeated factors of 165 and 333.
step 4 Find the product of repeated and non-repeated prime factors of 165 and 333:
= 3 x 5 x 11 x 3 x 37
= 18315
lcm(165 and 333) = 18315
Hence,
lcm of 165 and 333 is 18315
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 165 and 333.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 165 and 333
What to be found:
lcm (165, 333) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
165 and 333
step 3 Choose the divisor which divides each or most of the given integers (165 and 333), 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 333 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 165 | 333 |
| 3 | 55 | 111 |
| 5 | 55 | 37 |
| 11 | 11 | 37 |
| 37 | 1 | 37 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 165 and 333:
= 3 x 3 x 5 x 11 x 37
= 18315
LCM(165, 333) = 18315
The LCM of two numbers 165 and 333 is 18315