LCM of 205 and 345
14145 is the LCM of 205 and 345. 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 205 and 345, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 205 and 345?
lcm (205 345) = (?)
205 => 5 x 41
345 => 3 x 5 x 23
= 5 x 41 x 3 x 23
= 14145
lcm (205 and 345) = 14145
14145 is the LCM of 205 and 345.
where,
205 is a positive integer,
345 is a positive integer,
14145 is the LCM of 205 and 345,
{5} in {5 x 41, 3 x 5 x 23} is the common factors of 205 and 345,
{41 x 3 x 23} in {5 x 41, 3 x 5 x 23} are the uncommon factors of 205 and 345.
Use in Mathematics: LCM of 205 and 345
The below are some of the mathematical applications where lcm of 205 and 345 can be used:
- to find the least number which is exactly divisible by 205 and 345.
- to find the common denominator for two fractions having 205 and 345 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 205 and 345 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 205 seconds and bell B tolls at 345 seconds repeatedly. The answer is that all bells A and B toll together at 14145 seconds for the first time, at 28290 seconds for the second time, at 42435 seconds for the third time and so on.
Important Notes: 205 and 345 lcm
The below are the important notes to be remembered while solving the lcm of 205 and 345:
- The common prime factors and the remaining prime factors of 205 and 345 should be multiplied to find the least common multiple of 205 and 345, when solving lcm by using prime factors method.
- The results of lcm of 205 and 345, and the lcm of 345 and 205 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 205 and 345?
The below solved example with step by step work shows how to find what is the lcm of 205 and 345 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 205 and 345?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 205
B = 345
What to be found:
find the lcm of 205 and 345
step 2 Find the prime factors of 205 and 345:
Prime factors of 205 = 5 x 41
Prime factors of 345 = 3 x 5 x 23
step 3 Identify the repeated and non-repeated prime factors of 205 and 345:
{5} is the most repeated factor and {41 x 3 x 23} are the non-repeated factors of 205 and 345.
step 4 Find the product of repeated and non-repeated prime factors of 205 and 345:
= 5 x 41 x 3 x 23
= 14145
lcm(205 and 345) = 14145
Hence,
lcm of 205 and 345 is 14145
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 205 and 345.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 205 and 345
What to be found:
lcm (205, 345) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
205 and 345
step 3 Choose the divisor which divides each or most of the given integers (205 and 345), 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 205 and 345 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 205 | 345 |
| 5 | 205 | 115 |
| 23 | 41 | 23 |
| 41 | 41 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 205 and 345:
= 3 x 5 x 23 x 41
= 14145
LCM(205, 345) = 14145
The LCM of two numbers 205 and 345 is 14145