LCM of 205 and 342
70110 is the LCM of 205 and 342. 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 342, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 205 and 342?
lcm (205 342) = (?)
205 => 5 x 41
342 => 2 x 3 x 3 x 19
= 5 x 41 x 2 x 3 x 3 x 19
= 70110
lcm (205 and 342) = 70110
70110 is the LCM of 205 and 342.
where,
205 is a positive integer,
342 is a positive integer,
70110 is the LCM of 205 and 342,
There is no common factors of 205 and 342 in {5 x 41, 2 x 3 x 3 x 19},
{5 x 41 x 2 x 3 x 3 x 19} in {5 x 41, 2 x 3 x 3 x 19} are the uncommon factors of 205 and 342.
Use in Mathematics: LCM of 205 and 342
The below are some of the mathematical applications where lcm of 205 and 342 can be used:
- to find the least number which is exactly divisible by 205 and 342.
- to find the common denominator for two fractions having 205 and 342 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 205 and 342 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 342 seconds repeatedly. The answer is that all bells A and B toll together at 70110 seconds for the first time, at 140220 seconds for the second time, at 210330 seconds for the third time and so on.
Important Notes: 205 and 342 lcm
The below are the important notes to be remembered while solving the lcm of 205 and 342:
- The common prime factors and the remaining prime factors of 205 and 342 should be multiplied to find the least common multiple of 205 and 342, when solving lcm by using prime factors method.
- The results of lcm of 205 and 342, and the lcm of 342 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 342?
The below solved example with step by step work shows how to find what is the lcm of 205 and 342 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 205 and 342?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 205
B = 342
What to be found:
find the lcm of 205 and 342
step 2 Find the prime factors of 205 and 342:
Prime factors of 205 = 5 x 41
Prime factors of 342 = 2 x 3 x 3 x 19
step 3Identify the repeated and non-repeated prime factors of 205 and 342:
Since there is no common factors between 205 and 342, multiplying the given numbers directly provides the LCM of
205 and 342.
= 205 x 342
= 70110
lcm(205 and 342) = 70110
Hence,
lcm of 205 and 342 is 70110
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 205 and 342.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 205 and 342
What to be found:
lcm (205, 342) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
205 and 342
step 3 Choose the divisor which divides each or most of the given integers (205 and 342), 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 342 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 205 | 342 |
| 3 | 205 | 171 |
| 3 | 205 | 57 |
| 5 | 205 | 19 |
| 19 | 41 | 19 |
| 41 | 41 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 205 and 342:
= 2 x 3 x 3 x 5 x 19 x 41
= 70110
LCM(205, 342) = 70110
The LCM of two numbers 205 and 342 is 70110