LCM of 245 and 317
77665 is the LCM of 245 and 317. 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 245 and 317, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 245 and 317?
lcm (245 317) = (?)
245 => 5 x 7 x 7
317 => 317
= 5 x 7 x 7 x 317
= 77665
lcm (245 and 317) = 77665
77665 is the LCM of 245 and 317.
where,
245 is a positive integer,
317 is a positive integer,
77665 is the LCM of 245 and 317,
There is no common factors of 245 and 317 in {5 x 7 x 7, 317},
{5 x 7 x 7 x 317} in {5 x 7 x 7, 317} are the uncommon factors of 245 and 317.
Use in Mathematics: LCM of 245 and 317
The below are some of the mathematical applications where lcm of 245 and 317 can be used:
- to find the least number which is exactly divisible by 245 and 317.
- to find the common denominator for two fractions having 245 and 317 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 245 and 317 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 245 seconds and bell B tolls at 317 seconds repeatedly. The answer is that all bells A and B toll together at 77665 seconds for the first time, at 155330 seconds for the second time, at 232995 seconds for the third time and so on.
Important Notes: 245 and 317 lcm
The below are the important notes to be remembered while solving the lcm of 245 and 317:
- The common prime factors and the remaining prime factors of 245 and 317 should be multiplied to find the least common multiple of 245 and 317, when solving lcm by using prime factors method.
- The results of lcm of 245 and 317, and the lcm of 317 and 245 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 245 and 317?
The below solved example with step by step work shows how to find what is the lcm of 245 and 317 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 245 and 317?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 245
B = 317
What to be found:
find the lcm of 245 and 317
step 2 Find the prime factors of 245 and 317:
Prime factors of 245 = 5 x 7 x 7
Prime factors of 317 = 317
step 3Identify the repeated and non-repeated prime factors of 245 and 317:
Since there is no common factors between 245 and 317, multiplying the given numbers directly provides the LCM of
245 and 317.
= 245 x 317
= 77665
lcm(245 and 317) = 77665
Hence,
lcm of 245 and 317 is 77665
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 245 and 317.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 245 and 317
What to be found:
lcm (245, 317) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
245 and 317
step 3 Choose the divisor which divides each or most of the given integers (245 and 317), 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 245 and 317 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 5 | 245 | 317 |
| 7 | 49 | 317 |
| 7 | 7 | 317 |
| 317 | 1 | 317 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 245 and 317:
= 5 x 7 x 7 x 317
= 77665
LCM(245, 317) = 77665
The LCM of two numbers 245 and 317 is 77665