LCM of 257 and 321
82497 is the LCM of 257 and 321. 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 257 and 321, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 257 and 321?
lcm (257 321) = (?)
257 => 257
321 => 3 x 107
= 257 x 3 x 107
= 82497
lcm (257 and 321) = 82497
82497 is the LCM of 257 and 321.
where,
257 is a positive integer,
321 is a positive integer,
82497 is the LCM of 257 and 321,
There is no common factors of 257 and 321 in {257, 3 x 107},
{257 x 3 x 107} in {257, 3 x 107} are the uncommon factors of 257 and 321.
Use in Mathematics: LCM of 257 and 321
The below are some of the mathematical applications where lcm of 257 and 321 can be used:
- to find the least number which is exactly divisible by 257 and 321.
- to find the common denominator for two fractions having 257 and 321 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 257 and 321 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 257 seconds and bell B tolls at 321 seconds repeatedly. The answer is that all bells A and B toll together at 82497 seconds for the first time, at 164994 seconds for the second time, at 247491 seconds for the third time and so on.
Important Notes: 257 and 321 lcm
The below are the important notes to be remembered while solving the lcm of 257 and 321:
- The common prime factors and the remaining prime factors of 257 and 321 should be multiplied to find the least common multiple of 257 and 321, when solving lcm by using prime factors method.
- The results of lcm of 257 and 321, and the lcm of 321 and 257 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 257 and 321?
The below solved example with step by step work shows how to find what is the lcm of 257 and 321 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 257 and 321?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 257
B = 321
What to be found:
find the lcm of 257 and 321
step 2 Find the prime factors of 257 and 321:
Prime factors of 257 = 257
Prime factors of 321 = 3 x 107
step 3Identify the repeated and non-repeated prime factors of 257 and 321:
Since there is no common factors between 257 and 321, multiplying the given numbers directly provides the LCM of
257 and 321.
= 257 x 321
= 82497
lcm(257 and 321) = 82497
Hence,
lcm of 257 and 321 is 82497
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 257 and 321.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 257 and 321
What to be found:
lcm (257, 321) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
257 and 321
step 3 Choose the divisor which divides each or most of the given integers (257 and 321), 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 257 and 321 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 257 | 321 |
| 107 | 257 | 107 |
| 257 | 257 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 257 and 321:
= 3 x 107 x 257
= 82497
LCM(257, 321) = 82497
The LCM of two numbers 257 and 321 is 82497