LCM of 84 and 85
7140 is the LCM of 84 and 85. 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 85, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 84 and 85?
lcm (84 85) = (?)
84 => 2 x 2 x 3 x 7
85 => 5 x 17
= 2 x 2 x 3 x 7 x 5 x 17
= 7140
lcm (84 and 85) = 7140
7140 is the LCM of 84 and 85.
where,
84 is a positive integer,
85 is a positive integer,
7140 is the LCM of 84 and 85,
There is no common factors of 84 and 85 in {2 x 2 x 3 x 7, 5 x 17},
{2 x 2 x 3 x 7 x 5 x 17} in {2 x 2 x 3 x 7, 5 x 17} are the uncommon factors of 84 and 85.
Use in Mathematics: LCM of 84 and 85
The below are some of the mathematical applications where lcm of 84 and 85 can be used:
- to find the least number which is exactly divisible by 84 and 85.
- to find the common denominator for two fractions having 84 and 85 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 84 and 85 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 85 seconds repeatedly. The answer is that all bells A and B toll together at 7140 seconds for the first time, at 14280 seconds for the second time, at 21420 seconds for the third time and so on.
Important Notes: 84 and 85 lcm
The below are the important notes to be remembered while solving the lcm of 84 and 85:
- The common prime factors and the remaining prime factors of 84 and 85 should be multiplied to find the least common multiple of 84 and 85, when solving lcm by using prime factors method.
- The results of lcm of 84 and 85, and the lcm of 85 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 85?
The below solved example with step by step work shows how to find what is the lcm of 84 and 85 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 84 and 85?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 84
B = 85
What to be found:
find the lcm of 84 and 85
step 2 Find the prime factors of 84 and 85:
Prime factors of 84 = 2 x 2 x 3 x 7
Prime factors of 85 = 5 x 17
step 3Identify the repeated and non-repeated prime factors of 84 and 85:
Since there is no common factors between 84 and 85, multiplying the given numbers directly provides the LCM of
84 and 85.
= 84 x 85
= 7140
lcm(84 and 85) = 7140
Hence,
lcm of 84 and 85 is 7140
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 84 and 85.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 84 and 85
What to be found:
lcm (84, 85) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
84 and 85
step 3 Choose the divisor which divides each or most of the given integers (84 and 85), 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 85 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 84 | 85 |
| 2 | 42 | 85 |
| 3 | 21 | 85 |
| 5 | 7 | 85 |
| 7 | 7 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 84 and 85:
= 2 x 2 x 3 x 5 x 7 x 17
= 7140
LCM(84, 85) = 7140
The LCM of two numbers 84 and 85 is 7140