192 and 200 LCM
LCM of 192 and 200 is equal to 4800. The comprehensive work provides more insight of how to find what is the lcm of 192 and 200 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 192 and 200?
lcm (192 200) = (?)
192 => 2 x 2 x 2 x 2 x 2 x 2 x 3
200 => 2 x 2 x 2 x 5 x 5
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5
= 4800
lcm (192 and 200) = 4800
4800 is the lcm of 192 and 200.
where,
192 is a positive integer,
200 is a positive integer,
4800 is the lcm of 192 and 200,
{2 x 2 x 2} in {2 x 2 x 2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 5 x 5} are the common factors of 192 and 200,
{2 x 2 x 2 x 3 x 5 x 5} in {2 x 2 x 2 x 2 x 2 x 2 x 3, 2 x 2 x 2 x 5 x 5} are the uncommon factors of 192 and 200.
Use in Mathematics: LCM of 192 and 200
The below are some of the mathematical applications where lcm of 192 and 200 can be used:
- to find the least number which is exactly divisible by 192 and 200.
- to find the common denominator for two fractions having 192 and 200 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 192 and 200 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 200 seconds repeatedly. The answer is that all bells A and B toll together at 4800 seconds for the first time, at 9600 seconds for the second time, at 14400 seconds for the third time and so on.
Important Notes: 192 and 200 lcm
The below are the important notes to be remembered while solving the lcm of 192 and 200:
- The common prime factors and the remaining prime factors of 192 and 200 should be multiplied to find the least common multiple of 192 and 200, when solving lcm by using prime factors method.
- The results of lcm of 192 and 200, and the lcm of 200 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 200?
The below solved example with step by step work shows how to find what is the lcm of 192 and 200 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 192 and 200?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 192
B = 200
What to be found:
find the lcm of 192 and 200
step 2 Find the prime factors of 192 and 200:
Prime factors of 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3
Prime factors of 200 = 2 x 2 x 2 x 5 x 5
step 3 Identify the repeated and non-repeated prime factors of 192 and 200:
{2, 2, 2} are the most repeated factors and {2 x 2 x 2 x 3 x 5 x 5} are the non-repeated factors of 192 and 200.
step 4 Find the product of repeated and non-repeated prime factors of 192 and 200:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5
= 4800
lcm(192 and 200) = 4800
Hence,
lcm of 192 and 200 is 4800
This special division method is the easiest way to understand the entire calculation of what is the lcm of 192 and 200.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 192 and 200
What to be found:
lcm (192, 200) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
192 and 200
step 3 Choose the divisor which divides each or most of the given integers (192 and 200), 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 200 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 192 | 200 |
| 2 | 96 | 100 |
| 2 | 48 | 50 |
| 2 | 24 | 25 |
| 2 | 12 | 25 |
| 2 | 6 | 25 |
| 3 | 3 | 25 |
| 5 | 1 | 25 |
| 5 | 1 | 5 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 192 and 200:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5
= 4800
LCM(192, 200) = 4800
The least common multiple for two numbers 192 and 200 is 4800