LCM of 192 and 323
62016 is the LCM of 192 and 323. 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 323, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 192 and 323?
lcm (192 323) = (?)
192 => 2 x 2 x 2 x 2 x 2 x 2 x 3
323 => 17 x 19
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 17 x 19
= 62016
lcm (192 and 323) = 62016
62016 is the LCM of 192 and 323.
where,
192 is a positive integer,
323 is a positive integer,
62016 is the LCM of 192 and 323,
There is no common factors of 192 and 323 in {2 x 2 x 2 x 2 x 2 x 2 x 3, 17 x 19},
{2 x 2 x 2 x 2 x 2 x 2 x 3 x 17 x 19} in {2 x 2 x 2 x 2 x 2 x 2 x 3, 17 x 19} are the uncommon factors of 192 and 323.
Use in Mathematics: LCM of 192 and 323
The below are some of the mathematical applications where lcm of 192 and 323 can be used:
- to find the least number which is exactly divisible by 192 and 323.
- to find the common denominator for two fractions having 192 and 323 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 192 and 323 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 323 seconds repeatedly. The answer is that all bells A and B toll together at 62016 seconds for the first time, at 124032 seconds for the second time, at 186048 seconds for the third time and so on.
Important Notes: 192 and 323 lcm
The below are the important notes to be remembered while solving the lcm of 192 and 323:
- The common prime factors and the remaining prime factors of 192 and 323 should be multiplied to find the least common multiple of 192 and 323, when solving lcm by using prime factors method.
- The results of lcm of 192 and 323, and the lcm of 323 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 323?
The below solved example with step by step work shows how to find what is the lcm of 192 and 323 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 192 and 323?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 192
B = 323
What to be found:
find the lcm of 192 and 323
step 2 Find the prime factors of 192 and 323:
Prime factors of 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3
Prime factors of 323 = 17 x 19
step 3Identify the repeated and non-repeated prime factors of 192 and 323:
Since there is no common factors between 192 and 323, multiplying the given numbers directly provides the LCM of
192 and 323.
= 192 x 323
= 62016
lcm(192 and 323) = 62016
Hence,
lcm of 192 and 323 is 62016
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 192 and 323.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 192 and 323
What to be found:
lcm (192, 323) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
192 and 323
step 3 Choose the divisor which divides each or most of the given integers (192 and 323), 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 323 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 192 | 323 |
| 2 | 96 | 323 |
| 2 | 48 | 323 |
| 2 | 24 | 323 |
| 2 | 12 | 323 |
| 2 | 6 | 323 |
| 3 | 3 | 323 |
| 17 | 1 | 323 |
| 19 | 1 | 19 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 192 and 323:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 17 x 19
= 62016
LCM(192, 323) = 62016
The LCM of two numbers 192 and 323 is 62016