LCM of 8 and 214
856 is the LCM of 8 and 214. 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 8 and 214, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 8 and 214?
lcm (8 214) = (?)
8 => 2 x 2 x 2
214 => 2 x 107
= 2 x 2 x 2 x 107
= 856
lcm (8 and 214) = 856
856 is the LCM of 8 and 214.
where,
8 is a positive integer,
214 is a positive integer,
856 is the LCM of 8 and 214,
{2} in {2 x 2 x 2, 2 x 107} is the common factors of 8 and 214,
{2 x 2 x 107} in {2 x 2 x 2, 2 x 107} are the uncommon factors of 8 and 214.
Use in Mathematics: LCM of 8 and 214
The below are some of the mathematical applications where lcm of 8 and 214 can be used:
- to find the least number which is exactly divisible by 8 and 214.
- to find the common denominator for two fractions having 8 and 214 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 8 and 214 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 8 seconds and bell B tolls at 214 seconds repeatedly. The answer is that all bells A and B toll together at 856 seconds for the first time, at 1712 seconds for the second time, at 2568 seconds for the third time and so on.
Important Notes: 8 and 214 lcm
The below are the important notes to be remembered while solving the lcm of 8 and 214:
- The common prime factors and the remaining prime factors of 8 and 214 should be multiplied to find the least common multiple of 8 and 214, when solving lcm by using prime factors method.
- The results of lcm of 8 and 214, and the lcm of 214 and 8 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 8 and 214?
The below solved example with step by step work shows how to find what is the lcm of 8 and 214 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 8 and 214?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 8
B = 214
What to be found:
find the lcm of 8 and 214
step 2 Find the prime factors of 8 and 214:
Prime factors of 8 = 2 x 2 x 2
Prime factors of 214 = 2 x 107
step 3 Identify the repeated and non-repeated prime factors of 8 and 214:
{2} is the most repeated factor and {2 x 2 x 107} are the non-repeated factors of 8 and 214.
step 4 Find the product of repeated and non-repeated prime factors of 8 and 214:
= 2 x 2 x 2 x 107
= 856
lcm(8 and 214) = 856
Hence,
lcm of 8 and 214 is 856
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 8 and 214.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 8 and 214
What to be found:
lcm (8, 214) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
8 and 214
step 3 Choose the divisor which divides each or most of the given integers (8 and 214), 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 8 and 214 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 8 | 214 |
| 2 | 4 | 107 |
| 2 | 2 | 107 |
| 107 | 1 | 107 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 8 and 214:
= 2 x 2 x 2 x 107
= 856
LCM(8, 214) = 856
The LCM of two numbers 8 and 214 is 856