LCM of 256 and 328
10496 is the LCM of 256 and 328. 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 256 and 328, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 256 and 328?
lcm (256 328) = (?)
256 => 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
328 => 2 x 2 x 2 x 41
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 41
= 10496
lcm (256 and 328) = 10496
10496 is the LCM of 256 and 328.
where,
256 is a positive integer,
328 is a positive integer,
10496 is the LCM of 256 and 328,
{2 x 2 x 2} in {2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, 2 x 2 x 2 x 41} are the common factors of 256 and 328,
{2 x 2 x 2 x 2 x 2 x 41} in {2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, 2 x 2 x 2 x 41} are the uncommon factors of 256 and 328.
Use in Mathematics: LCM of 256 and 328
The below are some of the mathematical applications where lcm of 256 and 328 can be used:
- to find the least number which is exactly divisible by 256 and 328.
- to find the common denominator for two fractions having 256 and 328 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 256 and 328 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 256 seconds and bell B tolls at 328 seconds repeatedly. The answer is that all bells A and B toll together at 10496 seconds for the first time, at 20992 seconds for the second time, at 31488 seconds for the third time and so on.
Important Notes: 256 and 328 lcm
The below are the important notes to be remembered while solving the lcm of 256 and 328:
- The common prime factors and the remaining prime factors of 256 and 328 should be multiplied to find the least common multiple of 256 and 328, when solving lcm by using prime factors method.
- The results of lcm of 256 and 328, and the lcm of 328 and 256 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 256 and 328?
The below solved example with step by step work shows how to find what is the lcm of 256 and 328 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 256 and 328?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 256
B = 328
What to be found:
find the lcm of 256 and 328
step 2 Find the prime factors of 256 and 328:
Prime factors of 256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
Prime factors of 328 = 2 x 2 x 2 x 41
step 3 Identify the repeated and non-repeated prime factors of 256 and 328:
{2, 2, 2} are the most repeated factors and {2 x 2 x 2 x 2 x 2 x 41} are the non-repeated factors of 256 and 328.
step 4 Find the product of repeated and non-repeated prime factors of 256 and 328:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 41
= 10496
lcm(256 and 328) = 10496
Hence,
lcm of 256 and 328 is 10496
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 256 and 328.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 256 and 328
What to be found:
lcm (256, 328) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
256 and 328
step 3 Choose the divisor which divides each or most of the given integers (256 and 328), 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 256 and 328 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 256 | 328 |
| 2 | 128 | 164 |
| 2 | 64 | 82 |
| 2 | 32 | 41 |
| 2 | 16 | 41 |
| 2 | 8 | 41 |
| 2 | 4 | 41 |
| 2 | 2 | 41 |
| 41 | 1 | 41 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 256 and 328:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 41
= 10496
LCM(256, 328) = 10496
The LCM of two numbers 256 and 328 is 10496