LCM of 84 and 337
28308 is the LCM of 84 and 337. 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 337, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 84 and 337?
lcm (84 337) = (?)
84 => 2 x 2 x 3 x 7
337 => 337
= 2 x 2 x 3 x 7 x 337
= 28308
lcm (84 and 337) = 28308
28308 is the LCM of 84 and 337.
where,
84 is a positive integer,
337 is a positive integer,
28308 is the LCM of 84 and 337,
There is no common factors of 84 and 337 in {2 x 2 x 3 x 7, 337},
{2 x 2 x 3 x 7 x 337} in {2 x 2 x 3 x 7, 337} are the uncommon factors of 84 and 337.
Use in Mathematics: LCM of 84 and 337
The below are some of the mathematical applications where lcm of 84 and 337 can be used:
- to find the least number which is exactly divisible by 84 and 337.
- to find the common denominator for two fractions having 84 and 337 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 337 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 337 seconds repeatedly. The answer is that all bells A and B toll together at 28308 seconds for the first time, at 56616 seconds for the second time, at 84924 seconds for the third time and so on.
Important Notes: 84 and 337 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 337:
- The common prime factors and the remaining prime factors of 84 and 337 should be multiplied to find the least common multiple of 84 and 337, when solving lcm by using prime factors method.
- The results of lcm of 84 and 337, and the lcm of 337 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 337?
The below solved example with step by step work shows how to find what is the lcm of 84 and 337 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 337?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 337
What to be found:
find the lcm of 84 and 337
step 2 Find the prime factors of 84 and 337:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 337 = 337
step 3Identify the repeated and non-repeated prime factors of 84 and 337:
Since there is no common factors between 84 and 337, multiplying the given numbers directly provides the LCM of
84 and 337.
= 84 x 337
= 28308
lcm(84 and 337) = 28308
Hence,
lcm of 84 and 337 is 28308
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 84 and 337.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 337
What to be found:
lcm (84, 337) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 337
step 3 Choose the divisor which divides each or most of the given integers (84 and 337), 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 337 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 337 |
| 2 | 42 | 337 |
| 3 | 21 | 337 |
| 7 | 7 | 337 |
| 337 | 1 | 337 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 337:
= 2 x 2 x 3 x 7 x 337
= 28308
LCM(84, 337) = 28308
The LCM of two numbers 84 and 337 is 28308