LCM of 105 and 339
11865 is the LCM of 105 and 339. 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 105 and 339, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 105 and 339?
lcm (105 339) = (?)
105 => 3 x 5 x 7
339 => 3 x 113
= 3 x 5 x 7 x 113
= 11865
lcm (105 and 339) = 11865
11865 is the LCM of 105 and 339.
where,
105 is a positive integer,
339 is a positive integer,
11865 is the LCM of 105 and 339,
{3} in {3 x 5 x 7, 3 x 113} is the common factors of 105 and 339,
{5 x 7 x 113} in {3 x 5 x 7, 3 x 113} are the uncommon factors of 105 and 339.
Use in Mathematics: LCM of 105 and 339
The below are some of the mathematical applications where lcm of 105 and 339 can be used:
- to find the least number which is exactly divisible by 105 and 339.
- to find the common denominator for two fractions having 105 and 339 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 105 and 339 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 105 seconds and bell B tolls at 339 seconds repeatedly. The answer is that all bells A and B toll together at 11865 seconds for the first time, at 23730 seconds for the second time, at 35595 seconds for the third time and so on.
Important Notes: 105 and 339 lcm
The below are the important notes to be remembered while solving the lcm of 105 and 339:
- The common prime factors and the remaining prime factors of 105 and 339 should be multiplied to find the least common multiple of 105 and 339, when solving lcm by using prime factors method.
- The results of lcm of 105 and 339, and the lcm of 339 and 105 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 105 and 339?
The below solved example with step by step work shows how to find what is the lcm of 105 and 339 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 105 and 339?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 105
B = 339
What to be found:
find the lcm of 105 and 339
step 2 Find the prime factors of 105 and 339:
Prime factors of 105 = 3 x 5 x 7
Prime factors of 339 = 3 x 113
step 3 Identify the repeated and non-repeated prime factors of 105 and 339:
{3} is the most repeated factor and {5 x 7 x 113} are the non-repeated factors of 105 and 339.
step 4 Find the product of repeated and non-repeated prime factors of 105 and 339:
= 3 x 5 x 7 x 113
= 11865
lcm(105 and 339) = 11865
Hence,
lcm of 105 and 339 is 11865
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 105 and 339.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 105 and 339
What to be found:
lcm (105, 339) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
105 and 339
step 3 Choose the divisor which divides each or most of the given integers (105 and 339), 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 105 and 339 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 105 | 339 |
| 5 | 35 | 113 |
| 7 | 7 | 113 |
| 113 | 1 | 113 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 105 and 339:
= 3 x 5 x 7 x 113
= 11865
LCM(105, 339) = 11865
The LCM of two numbers 105 and 339 is 11865