LCM of 84 and 137
11508 is the LCM of 84 and 137. 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 137, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 84 and 137?
lcm (84 137) = (?)
84 => 2 x 2 x 3 x 7
137 => 137
= 2 x 2 x 3 x 7 x 137
= 11508
lcm (84 and 137) = 11508
11508 is the LCM of 84 and 137.
where,
84 is a positive integer,
137 is a positive integer,
11508 is the LCM of 84 and 137,
There is no common factors of 84 and 137 in {2 x 2 x 3 x 7, 137},
{2 x 2 x 3 x 7 x 137} in {2 x 2 x 3 x 7, 137} are the uncommon factors of 84 and 137.
Use in Mathematics: LCM of 84 and 137
The below are some of the mathematical applications where lcm of 84 and 137 can be used:
- to find the least number which is exactly divisible by 84 and 137.
- to find the common denominator for two fractions having 84 and 137 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 137 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 137 seconds repeatedly. The answer is that all bells A and B toll together at 11508 seconds for the first time, at 23016 seconds for the second time, at 34524 seconds for the third time and so on.
Important Notes: 84 and 137 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 137:
- The common prime factors and the remaining prime factors of 84 and 137 should be multiplied to find the least common multiple of 84 and 137, when solving lcm by using prime factors method.
- The results of lcm of 84 and 137, and the lcm of 137 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 137?
The below solved example with step by step work shows how to find what is the lcm of 84 and 137 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 137?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 137
What to be found:
find the lcm of 84 and 137
step 2 Find the prime factors of 84 and 137:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 137 = 137
step 3Identify the repeated and non-repeated prime factors of 84 and 137:
Since there is no common factors between 84 and 137, multiplying the given numbers directly provides the LCM of
84 and 137.
= 84 x 137
= 11508
lcm(84 and 137) = 11508
Hence,
lcm of 84 and 137 is 11508
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 84 and 137.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 137
What to be found:
lcm (84, 137) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 137
step 3 Choose the divisor which divides each or most of the given integers (84 and 137), 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 137 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 137 |
| 2 | 42 | 137 |
| 3 | 21 | 137 |
| 7 | 7 | 137 |
| 137 | 1 | 137 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 137:
= 2 x 2 x 3 x 7 x 137
= 11508
LCM(84, 137) = 11508
The LCM of two numbers 84 and 137 is 11508