LCM of 224 and 287
9184 is the LCM of 224 and 287. 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 224 and 287, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 224 and 287?
lcm (224 287) = (?)
224 => 2 x 2 x 2 x 2 x 2 x 7
287 => 7 x 41
= 7 x 2 x 2 x 2 x 2 x 2 x 41
= 9184
lcm (224 and 287) = 9184
9184 is the LCM of 224 and 287.
where,
224 is a positive integer,
287 is a positive integer,
9184 is the LCM of 224 and 287,
{7} in {2 x 2 x 2 x 2 x 2 x 7, 7 x 41} is the common factors of 224 and 287,
{2 x 2 x 2 x 2 x 2 x 41} in {2 x 2 x 2 x 2 x 2 x 7, 7 x 41} are the uncommon factors of 224 and 287.
Use in Mathematics: LCM of 224 and 287
The below are some of the mathematical applications where lcm of 224 and 287 can be used:
- to find the least number which is exactly divisible by 224 and 287.
- to find the common denominator for two fractions having 224 and 287 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 224 and 287 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 224 seconds and bell B tolls at 287 seconds repeatedly. The answer is that all bells A and B toll together at 9184 seconds for the first time, at 18368 seconds for the second time, at 27552 seconds for the third time and so on.
Important Notes: 224 and 287 lcm
The below are the important notes to be remembered while solving the lcm of 224 and 287:
- The common prime factors and the remaining prime factors of 224 and 287 should be multiplied to find the least common multiple of 224 and 287, when solving lcm by using prime factors method.
- The results of lcm of 224 and 287, and the lcm of 287 and 224 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 224 and 287?
The below solved example with step by step work shows how to find what is the lcm of 224 and 287 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 224 and 287?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 224
B = 287
What to be found:
find the lcm of 224 and 287
step 2 Find the prime factors of 224 and 287:
Prime factors of 224 = 2 x 2 x 2 x 2 x 2 x 7
Prime factors of 287 = 7 x 41
step 3 Identify the repeated and non-repeated prime factors of 224 and 287:
{7} is the most repeated factor and {2 x 2 x 2 x 2 x 2 x 41} are the non-repeated factors of 224 and 287.
step 4 Find the product of repeated and non-repeated prime factors of 224 and 287:
= 7 x 2 x 2 x 2 x 2 x 2 x 41
= 9184
lcm(224 and 287) = 9184
Hence,
lcm of 224 and 287 is 9184
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 224 and 287.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 224 and 287
What to be found:
lcm (224, 287) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
224 and 287
step 3 Choose the divisor which divides each or most of the given integers (224 and 287), 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 224 and 287 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 224 | 287 |
| 2 | 112 | 287 |
| 2 | 56 | 287 |
| 2 | 28 | 287 |
| 2 | 14 | 287 |
| 7 | 7 | 287 |
| 41 | 1 | 41 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 224 and 287:
= 2 x 2 x 2 x 2 x 2 x 7 x 41
= 9184
LCM(224, 287) = 9184
The LCM of two numbers 224 and 287 is 9184