LCM of 306 and 341
104346 is the LCM of 306 and 341. 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 306 and 341, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 306 and 341?
lcm (306 341) = (?)
306 => 2 x 3 x 3 x 17
341 => 11 x 31
= 2 x 3 x 3 x 17 x 11 x 31
= 104346
lcm (306 and 341) = 104346
104346 is the LCM of 306 and 341.
where,
306 is a positive integer,
341 is a positive integer,
104346 is the LCM of 306 and 341,
There is no common factors of 306 and 341 in {2 x 3 x 3 x 17, 11 x 31},
{2 x 3 x 3 x 17 x 11 x 31} in {2 x 3 x 3 x 17, 11 x 31} are the uncommon factors of 306 and 341.
Use in Mathematics: LCM of 306 and 341
The below are some of the mathematical applications where lcm of 306 and 341 can be used:
- to find the least number which is exactly divisible by 306 and 341.
- to find the common denominator for two fractions having 306 and 341 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 306 and 341 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 306 seconds and bell B tolls at 341 seconds repeatedly. The answer is that all bells A and B toll together at 104346 seconds for the first time, at 208692 seconds for the second time, at 313038 seconds for the third time and so on.
Important Notes: 306 and 341 lcm
The below are the important notes to be remembered while solving the lcm of 306 and 341:
- The common prime factors and the remaining prime factors of 306 and 341 should be multiplied to find the least common multiple of 306 and 341, when solving lcm by using prime factors method.
- The results of lcm of 306 and 341, and the lcm of 341 and 306 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 306 and 341?
The below solved example with step by step work shows how to find what is the lcm of 306 and 341 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 306 and 341?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 306
B = 341
What to be found:
find the lcm of 306 and 341
step 2 Find the prime factors of 306 and 341:
Prime factors of 306 = 2 x 3 x 3 x 17
Prime factors of 341 = 11 x 31
step 3Identify the repeated and non-repeated prime factors of 306 and 341:
Since there is no common factors between 306 and 341, multiplying the given numbers directly provides the LCM of
306 and 341.
= 306 x 341
= 104346
lcm(306 and 341) = 104346
Hence,
lcm of 306 and 341 is 104346
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 306 and 341.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 306 and 341
What to be found:
lcm (306, 341) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
306 and 341
step 3 Choose the divisor which divides each or most of the given integers (306 and 341), 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 306 and 341 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 306 | 341 |
| 3 | 153 | 341 |
| 3 | 51 | 341 |
| 11 | 17 | 341 |
| 17 | 17 | 31 |
| 31 | 1 | 31 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 306 and 341:
= 2 x 3 x 3 x 11 x 17 x 31
= 104346
LCM(306, 341) = 104346
The LCM of two numbers 306 and 341 is 104346