LCM of 82 and 346
14186 is the LCM of 82 and 346. 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 82 and 346, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 82 and 346?
lcm (82 346) = (?)
82 => 2 x 41
346 => 2 x 173
= 2 x 41 x 173
= 14186
lcm (82 and 346) = 14186
14186 is the LCM of 82 and 346.
where,
82 is a positive integer,
346 is a positive integer,
14186 is the LCM of 82 and 346,
{2} in {2 x 41, 2 x 173} is the common factors of 82 and 346,
{41 x 173} in {2 x 41, 2 x 173} are the uncommon factors of 82 and 346.
Use in Mathematics: LCM of 82 and 346
The below are some of the mathematical applications where lcm of 82 and 346 can be used:
- to find the least number which is exactly divisible by 82 and 346.
- to find the common denominator for two fractions having 82 and 346 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 82 and 346 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 82 seconds and bell B tolls at 346 seconds repeatedly. The answer is that all bells A and B toll together at 14186 seconds for the first time, at 28372 seconds for the second time, at 42558 seconds for the third time and so on.
Important Notes: 82 and 346 lcm
The below are the important notes to be remembered while solving the lcm of 82 and 346:
- The common prime factors and the remaining prime factors of 82 and 346 should be multiplied to find the least common multiple of 82 and 346, when solving lcm by using prime factors method.
- The results of lcm of 82 and 346, and the lcm of 346 and 82 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 82 and 346?
The below solved example with step by step work shows how to find what is the lcm of 82 and 346 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 82 and 346?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 82
B = 346
What to be found:
find the lcm of 82 and 346
step 2 Find the prime factors of 82 and 346:
Prime factors of 82 = 2 x 41
Prime factors of 346 = 2 x 173
step 3 Identify the repeated and non-repeated prime factors of 82 and 346:
{2} is the most repeated factor and {41 x 173} are the non-repeated factors of 82 and 346.
step 4 Find the product of repeated and non-repeated prime factors of 82 and 346:
= 2 x 41 x 173
= 14186
lcm(82 and 346) = 14186
Hence,
lcm of 82 and 346 is 14186
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 82 and 346.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 82 and 346
What to be found:
lcm (82, 346) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
82 and 346
step 3 Choose the divisor which divides each or most of the given integers (82 and 346), 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 82 and 346 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 82 | 346 |
| 41 | 41 | 173 |
| 173 | 1 | 173 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 82 and 346:
= 2 x 41 x 173
= 14186
LCM(82, 346) = 14186
The LCM of two numbers 82 and 346 is 14186