LCM of 85 and 96
8160 is the LCM of 85 and 96. 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 85 and 96, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 85 and 96?
lcm (85 96) = (?)
85 => 5 x 17
96 => 2 x 2 x 2 x 2 x 2 x 3
= 5 x 17 x 2 x 2 x 2 x 2 x 2 x 3
= 8160
lcm (85 and 96) = 8160
8160 is the LCM of 85 and 96.
where,
85 is a positive integer,
96 is a positive integer,
8160 is the LCM of 85 and 96,
There is no common factors of 85 and 96 in {5 x 17, 2 x 2 x 2 x 2 x 2 x 3},
{5 x 17 x 2 x 2 x 2 x 2 x 2 x 3} in {5 x 17, 2 x 2 x 2 x 2 x 2 x 3} are the uncommon factors of 85 and 96.
Use in Mathematics: LCM of 85 and 96
The below are some of the mathematical applications where lcm of 85 and 96 can be used:
- to find the least number which is exactly divisible by 85 and 96.
- to find the common denominator for two fractions having 85 and 96 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 85 and 96 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 85 seconds and bell B tolls at 96 seconds repeatedly. The answer is that all bells A and B toll together at 8160 seconds for the first time, at 16320 seconds for the second time, at 24480 seconds for the third time and so on.
Important Notes: 85 and 96 lcm
The below are the important notes to be remembered while solving the lcm of 85 and 96:
- The common prime factors and the remaining prime factors of 85 and 96 should be multiplied to find the least common multiple of 85 and 96, when solving lcm by using prime factors method.
- The results of lcm of 85 and 96, and the lcm of 96 and 85 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 85 and 96?
The below solved example with step by step work shows how to find what is the lcm of 85 and 96 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 85 and 96?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 85
B = 96
What to be found:
find the lcm of 85 and 96
step 2 Find the prime factors of 85 and 96:
Prime factors of 85 = 5 x 17
Prime factors of 96 = 2 x 2 x 2 x 2 x 2 x 3
step 3Identify the repeated and non-repeated prime factors of 85 and 96:
Since there is no common factors between 85 and 96, multiplying the given numbers directly provides the LCM of
85 and 96.
= 85 x 96
= 8160
lcm(85 and 96) = 8160
Hence,
lcm of 85 and 96 is 8160
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 85 and 96.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 85 and 96
What to be found:
lcm (85, 96) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
85 and 96
step 3 Choose the divisor which divides each or most of the given integers (85 and 96), 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 85 and 96 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 85 | 96 |
| 2 | 85 | 48 |
| 2 | 85 | 24 |
| 2 | 85 | 12 |
| 2 | 85 | 6 |
| 3 | 85 | 3 |
| 5 | 85 | 1 |
| 17 | 17 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 85 and 96:
= 2 x 2 x 2 x 2 x 2 x 3 x 5 x 17
= 8160
LCM(85, 96) = 8160
The LCM of two numbers 85 and 96 is 8160