LCM of 192 and 359
68928 is the LCM of 192 and 359. 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 192 and 359, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 192 and 359?
lcm (192 359) = (?)
192 => 2 x 2 x 2 x 2 x 2 x 2 x 3
359 => 359
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 359
= 68928
lcm (192 and 359) = 68928
68928 is the LCM of 192 and 359.
where,
192 is a positive integer,
359 is a positive integer,
68928 is the LCM of 192 and 359,
There is no common factors of 192 and 359 in {2 x 2 x 2 x 2 x 2 x 2 x 3, 359},
{2 x 2 x 2 x 2 x 2 x 2 x 3 x 359} in {2 x 2 x 2 x 2 x 2 x 2 x 3, 359} are the uncommon factors of 192 and 359.
Use in Mathematics: LCM of 192 and 359
The below are some of the mathematical applications where lcm of 192 and 359 can be used:
- to find the least number which is exactly divisible by 192 and 359.
- to find the common denominator for two fractions having 192 and 359 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 192 and 359 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 192 seconds and bell B tolls at 359 seconds repeatedly. The answer is that all bells A and B toll together at 68928 seconds for the first time, at 137856 seconds for the second time, at 206784 seconds for the third time and so on.
Important Notes: 192 and 359 lcm
The below are the important notes to be remembered while solving the lcm of 192 and 359:
- The common prime factors and the remaining prime factors of 192 and 359 should be multiplied to find the least common multiple of 192 and 359, when solving lcm by using prime factors method.
- The results of lcm of 192 and 359, and the lcm of 359 and 192 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 192 and 359?
The below solved example with step by step work shows how to find what is the lcm of 192 and 359 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 192 and 359?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 192
B = 359
What to be found:
find the lcm of 192 and 359
step 2 Find the prime factors of 192 and 359:
Prime factors of 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3
Prime factors of 359 = 359
step 3Identify the repeated and non-repeated prime factors of 192 and 359:
Since there is no common factors between 192 and 359, multiplying the given numbers directly provides the LCM of
192 and 359.
= 192 x 359
= 68928
lcm(192 and 359) = 68928
Hence,
lcm of 192 and 359 is 68928
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 192 and 359.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 192 and 359
What to be found:
lcm (192, 359) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
192 and 359
step 3 Choose the divisor which divides each or most of the given integers (192 and 359), 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 192 and 359 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 192 | 359 |
| 2 | 96 | 359 |
| 2 | 48 | 359 |
| 2 | 24 | 359 |
| 2 | 12 | 359 |
| 2 | 6 | 359 |
| 3 | 3 | 359 |
| 359 | 1 | 359 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 192 and 359:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 359
= 68928
LCM(192, 359) = 68928
The LCM of two numbers 192 and 359 is 68928