LCM of 84 and 284
5964 is the LCM of 84 and 284. 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 84 and 284, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 84 and 284?
lcm (84 284) = (?)
84 => 2 x 2 x 3 x 7
284 => 2 x 2 x 71
= 2 x 2 x 3 x 7 x 71
= 5964
lcm (84 and 284) = 5964
5964 is the LCM of 84 and 284.
where,
84 is a positive integer,
284 is a positive integer,
5964 is the LCM of 84 and 284,
{2 x 2} in {2 x 2 x 3 x 7, 2 x 2 x 71} are the common factors of 84 and 284,
{3 x 7 x 71} in {2 x 2 x 3 x 7, 2 x 2 x 71} are the uncommon factors of 84 and 284.
Use in Mathematics: LCM of 84 and 284
The below are some of the mathematical applications where lcm of 84 and 284 can be used:
- to find the least number which is exactly divisible by 84 and 284.
- to find the common denominator for two fractions having 84 and 284 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 284 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 84 seconds and bell B tolls at 284 seconds repeatedly. The answer is that all bells A and B toll together at 5964 seconds for the first time, at 11928 seconds for the second time, at 17892 seconds for the third time and so on.
Important Notes: 84 and 284 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 284:
- The common prime factors and the remaining prime factors of 84 and 284 should be multiplied to find the least common multiple of 84 and 284, when solving lcm by using prime factors method.
- The results of lcm of 84 and 284, and the lcm of 284 and 84 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 84 and 284?
The below solved example with step by step work shows how to find what is the lcm of 84 and 284 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 284?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 284
What to be found:
find the lcm of 84 and 284
step 2 Find the prime factors of 84 and 284:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 284 = 2 x 2 x 71
step 3 Identify the repeated and non-repeated prime factors of 84 and 284:
{2, 2} are the most repeated factors and {3 x 7 x 71} are the non-repeated factors of 84 and 284.
step 4 Find the product of repeated and non-repeated prime factors of 84 and 284:
= 2 x 2 x 3 x 7 x 71
= 5964
lcm(84 and 284) = 5964
Hence,
lcm of 84 and 284 is 5964
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 84 and 284.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 284
What to be found:
lcm (84, 284) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 284
step 3 Choose the divisor which divides each or most of the given integers (84 and 284), 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 84 and 284 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 284 |
| 2 | 42 | 142 |
| 3 | 21 | 71 |
| 7 | 7 | 71 |
| 71 | 1 | 71 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 284:
= 2 x 2 x 3 x 7 x 71
= 5964
LCM(84, 284) = 5964
The LCM of two numbers 84 and 284 is 5964