LCM of 288 and 299
86112 is the LCM of 288 and 299. 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 288 and 299, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 288 and 299?
lcm (288 299) = (?)
288 => 2 x 2 x 2 x 2 x 2 x 3 x 3
299 => 13 x 23
= 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 23
= 86112
lcm (288 and 299) = 86112
86112 is the LCM of 288 and 299.
where,
288 is a positive integer,
299 is a positive integer,
86112 is the LCM of 288 and 299,
There is no common factors of 288 and 299 in {2 x 2 x 2 x 2 x 2 x 3 x 3, 13 x 23},
{2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 23} in {2 x 2 x 2 x 2 x 2 x 3 x 3, 13 x 23} are the uncommon factors of 288 and 299.
Use in Mathematics: LCM of 288 and 299
The below are some of the mathematical applications where lcm of 288 and 299 can be used:
- to find the least number which is exactly divisible by 288 and 299.
- to find the common denominator for two fractions having 288 and 299 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 288 and 299 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 288 seconds and bell B tolls at 299 seconds repeatedly. The answer is that all bells A and B toll together at 86112 seconds for the first time, at 172224 seconds for the second time, at 258336 seconds for the third time and so on.
Important Notes: 288 and 299 lcm
The below are the important notes to be remembered while solving the lcm of 288 and 299:
- The common prime factors and the remaining prime factors of 288 and 299 should be multiplied to find the least common multiple of 288 and 299, when solving lcm by using prime factors method.
- The results of lcm of 288 and 299, and the lcm of 299 and 288 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 288 and 299?
The below solved example with step by step work shows how to find what is the lcm of 288 and 299 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 288 and 299?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 288
B = 299
What to be found:
find the lcm of 288 and 299
step 2 Find the prime factors of 288 and 299:
Prime factors of 288 = 2 x 2 x 2 x 2 x 2 x 3 x 3
Prime factors of 299 = 13 x 23
step 3Identify the repeated and non-repeated prime factors of 288 and 299:
Since there is no common factors between 288 and 299, multiplying the given numbers directly provides the LCM of
288 and 299.
= 288 x 299
= 86112
lcm(288 and 299) = 86112
Hence,
lcm of 288 and 299 is 86112
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 288 and 299.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 288 and 299
What to be found:
lcm (288, 299) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
288 and 299
step 3 Choose the divisor which divides each or most of the given integers (288 and 299), 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 288 and 299 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 288 | 299 |
| 2 | 144 | 299 |
| 2 | 72 | 299 |
| 2 | 36 | 299 |
| 2 | 18 | 299 |
| 3 | 9 | 299 |
| 3 | 3 | 299 |
| 13 | 1 | 299 |
| 23 | 1 | 23 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 288 and 299:
= 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 23
= 86112
LCM(288, 299) = 86112
The LCM of two numbers 288 and 299 is 86112