LCM of 319 and 331
105589 is the LCM of 319 and 331. 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 319 and 331, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 319 and 331?
lcm (319 331) = (?)
319 => 11 x 29
331 => 331
= 11 x 29 x 331
= 105589
lcm (319 and 331) = 105589
105589 is the LCM of 319 and 331.
where,
319 is a positive integer,
331 is a positive integer,
105589 is the LCM of 319 and 331,
There is no common factors of 319 and 331 in {11 x 29, 331},
{11 x 29 x 331} in {11 x 29, 331} are the uncommon factors of 319 and 331.
Use in Mathematics: LCM of 319 and 331
The below are some of the mathematical applications where lcm of 319 and 331 can be used:
- to find the least number which is exactly divisible by 319 and 331.
- to find the common denominator for two fractions having 319 and 331 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 319 and 331 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 319 seconds and bell B tolls at 331 seconds repeatedly. The answer is that all bells A and B toll together at 105589 seconds for the first time, at 211178 seconds for the second time, at 316767 seconds for the third time and so on.
Important Notes: 319 and 331 lcm
The below are the important notes to be remembered while solving the lcm of 319 and 331:
- The common prime factors and the remaining prime factors of 319 and 331 should be multiplied to find the least common multiple of 319 and 331, when solving lcm by using prime factors method.
- The results of lcm of 319 and 331, and the lcm of 331 and 319 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 319 and 331?
The below solved example with step by step work shows how to find what is the lcm of 319 and 331 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 319 and 331?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 319
B = 331
What to be found:
find the lcm of 319 and 331
step 2 Find the prime factors of 319 and 331:
Prime factors of 319 = 11 x 29
Prime factors of 331 = 331
step 3Identify the repeated and non-repeated prime factors of 319 and 331:
Since there is no common factors between 319 and 331, multiplying the given numbers directly provides the LCM of
319 and 331.
= 319 x 331
= 105589
lcm(319 and 331) = 105589
Hence,
lcm of 319 and 331 is 105589
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 319 and 331.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 319 and 331
What to be found:
lcm (319, 331) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
319 and 331
step 3 Choose the divisor which divides each or most of the given integers (319 and 331), 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 319 and 331 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 11 | 319 | 331 |
| 29 | 29 | 331 |
| 331 | 1 | 331 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 319 and 331:
= 11 x 29 x 331
= 105589
LCM(319, 331) = 105589
The LCM of two numbers 319 and 331 is 105589