LCM of 208 and 286
2288 is the LCM of 208 and 286. 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 208 and 286, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 208 and 286?
lcm (208 286) = (?)
208 => 2 x 2 x 2 x 2 x 13
286 => 2 x 11 x 13
= 2 x 13 x 2 x 2 x 2 x 11
= 2288
lcm (208 and 286) = 2288
2288 is the LCM of 208 and 286.
where,
208 is a positive integer,
286 is a positive integer,
2288 is the LCM of 208 and 286,
{2 x 13} in {2 x 2 x 2 x 2 x 13, 2 x 11 x 13} are the common factors of 208 and 286,
{2 x 2 x 2 x 11} in {2 x 2 x 2 x 2 x 13, 2 x 11 x 13} are the uncommon factors of 208 and 286.
Use in Mathematics: LCM of 208 and 286
The below are some of the mathematical applications where lcm of 208 and 286 can be used:
- to find the least number which is exactly divisible by 208 and 286.
- to find the common denominator for two fractions having 208 and 286 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 208 and 286 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 208 seconds and bell B tolls at 286 seconds repeatedly. The answer is that all bells A and B toll together at 2288 seconds for the first time, at 4576 seconds for the second time, at 6864 seconds for the third time and so on.
Important Notes: 208 and 286 lcm
The below are the important notes to be remembered while solving the lcm of 208 and 286:
- The common prime factors and the remaining prime factors of 208 and 286 should be multiplied to find the least common multiple of 208 and 286, when solving lcm by using prime factors method.
- The results of lcm of 208 and 286, and the lcm of 286 and 208 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 208 and 286?
The below solved example with step by step work shows how to find what is the lcm of 208 and 286 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 208 and 286?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 208
B = 286
What to be found:
find the lcm of 208 and 286
step 2 Find the prime factors of 208 and 286:
Prime factors of 208 = 2 x 2 x 2 x 2 x 13
Prime factors of 286 = 2 x 11 x 13
step 3 Identify the repeated and non-repeated prime factors of 208 and 286:
{2, 13} are the most repeated factors and {2 x 2 x 2 x 11} are the non-repeated factors of 208 and 286.
step 4 Find the product of repeated and non-repeated prime factors of 208 and 286:
= 2 x 13 x 2 x 2 x 2 x 11
= 2288
lcm(208 and 286) = 2288
Hence,
lcm of 208 and 286 is 2288
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 208 and 286.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 208 and 286
What to be found:
lcm (208, 286) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
208 and 286
step 3 Choose the divisor which divides each or most of the given integers (208 and 286), 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 208 and 286 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 208 | 286 |
| 2 | 104 | 143 |
| 2 | 52 | 143 |
| 2 | 26 | 143 |
| 11 | 13 | 143 |
| 13 | 13 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 208 and 286:
= 2 x 2 x 2 x 2 x 11 x 13
= 2288
LCM(208, 286) = 2288
The LCM of two numbers 208 and 286 is 2288