128 and 194 LCM
LCM of 128 and 194 is equal to 12416. The comprehensive work provides more insight of how to find what is the lcm of 128 and 194 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 128 and 194?
lcm (128 194) = (?)
128 => 2 x 2 x 2 x 2 x 2 x 2 x 2
194 => 2 x 97
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 97
= 12416
lcm (128 and 194) = 12416
12416 is the lcm of 128 and 194.
where,
128 is a positive integer,
194 is a positive integer,
12416 is the lcm of 128 and 194,
{2} in {2 x 2 x 2 x 2 x 2 x 2 x 2, 2 x 97} is the common factors of 128 and 194,
{2 x 2 x 2 x 2 x 2 x 2 x 97} in {2 x 2 x 2 x 2 x 2 x 2 x 2, 2 x 97} are the uncommon factors of 128 and 194.
Use in Mathematics: LCM of 128 and 194
The below are some of the mathematical applications where lcm of 128 and 194 can be used:
- to find the least number which is exactly divisible by 128 and 194.
- to find the common denominator for two fractions having 128 and 194 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 128 and 194 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 128 seconds and bell B tolls at 194 seconds repeatedly. The answer is that all bells A and B toll together at 12416 seconds for the first time, at 24832 seconds for the second time, at 37248 seconds for the third time and so on.
Important Notes: 128 and 194 lcm
The below are the important notes to be remembered while solving the lcm of 128 and 194:
- The common prime factors and the remaining prime factors of 128 and 194 should be multiplied to find the least common multiple of 128 and 194, when solving lcm by using prime factors method.
- The results of lcm of 128 and 194, and the lcm of 194 and 128 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 128 and 194?
Solved example using prime factors method:
What is the LCM of 128 and 194?
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 128
B = 194
What to be found:
find the lcm of 128 and 194
step 2 Find the prime factors of 128 and 194:
Prime factors of 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
Prime factors of 194 = 2 x 97
step 3 Identify the repeated and non-repeated prime factors of 128 and 194:
{2} is the most repeated factor and {2 x 2 x 2 x 2 x 2 x 2 x 97} are the non-repeated factors of 128 and 194.
step 4 Find the product of repeated and non-repeated prime factors of 128 and 194:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 97
= 12416
lcm(128 and 194) = 12416
Hence,
lcm of 128 and 194 is 12416
This special division method is the easiest way to understand the entire calculation of what is the lcm of 128 and 194.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 128 and 194
What to be found:
lcm (128, 194) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
128 and 194
step 3 Choose the divisor which divides each or most of the given integers (128 and 194), 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 128 and 194 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 128 | 194 |
| 2 | 64 | 97 |
| 2 | 32 | 97 |
| 2 | 16 | 97 |
| 2 | 8 | 97 |
| 2 | 4 | 97 |
| 2 | 2 | 97 |
| 97 | 1 | 97 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 128 and 194:
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 97
= 12416
LCM(128, 194) = 12416
The least common multiple for two numbers 128 and 194 is 12416
