LCM of 165 and 170
5610 is the LCM of 165 and 170. 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 170, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 165 and 170?
lcm (165 170) = (?)
165 => 3 x 5 x 11
170 => 2 x 5 x 17
= 5 x 3 x 11 x 2 x 17
= 5610
lcm (165 and 170) = 5610
5610 is the LCM of 165 and 170.
where,
165 is a positive integer,
170 is a positive integer,
5610 is the LCM of 165 and 170,
{5} in {3 x 5 x 11, 2 x 5 x 17} is the common factors of 165 and 170,
{3 x 11 x 2 x 17} in {3 x 5 x 11, 2 x 5 x 17} are the uncommon factors of 165 and 170.
Use in Mathematics: LCM of 165 and 170
The below are some of the mathematical applications where lcm of 165 and 170 can be used:
- to find the least number which is exactly divisible by 165 and 170.
- to find the common denominator for two fractions having 165 and 170 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 165 and 170 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 170 seconds repeatedly. The answer is that all bells A and B toll together at 5610 seconds for the first time, at 11220 seconds for the second time, at 16830 seconds for the third time and so on.
Important Notes: 165 and 170 lcm
The below are the important notes to be remembered while solving the lcm of 165 and 170:
- The common prime factors and the remaining prime factors of 165 and 170 should be multiplied to find the least common multiple of 165 and 170, when solving lcm by using prime factors method.
- The results of lcm of 165 and 170, and the lcm of 170 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 170?
The below solved example with step by step work shows how to find what is the lcm of 165 and 170 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 165 and 170?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 165
B = 170
What to be found:
find the lcm of 165 and 170
step 2 Find the prime factors of 165 and 170:
Prime factors of 165 = 3 x 5 x 11
Prime factors of 170 = 2 x 5 x 17
step 3 Identify the repeated and non-repeated prime factors of 165 and 170:
{5} is the most repeated factor and {3 x 11 x 2 x 17} are the non-repeated factors of 165 and 170.
step 4 Find the product of repeated and non-repeated prime factors of 165 and 170:
= 5 x 3 x 11 x 2 x 17
= 5610
lcm(165 and 170) = 5610
Hence,
lcm of 165 and 170 is 5610
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 165 and 170.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 165 and 170
What to be found:
lcm (165, 170) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
165 and 170
step 3 Choose the divisor which divides each or most of the given integers (165 and 170), 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 170 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 165 | 170 |
| 3 | 165 | 85 |
| 5 | 55 | 85 |
| 11 | 11 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 165 and 170:
= 2 x 3 x 5 x 11 x 17
= 5610
LCM(165, 170) = 5610
The LCM of two numbers 165 and 170 is 5610