LCM of 85, 86 and 93
679830 is the LCM of 85, 86 and 93. 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, 86 and 93, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 85, 86 and 93?
lcm (85 86 93) = (?)
85 => 5 x 17
86 => 2 x 43
93 => 3 x 31
= 5 x 17 x 2 x 43 x 3 x 31
= 679830
lcm (85, 86 and 93) = 679830
The LCM of 85, 86 and 93 is 679830
where,
85 is a positive integer,
86 is a positive integer,
679830 is the LCM of 85, 86 and 93,
in {5 x 17, 2 x 43, 3 x 31} there is no repeated factors of 85, 86 and 93,
{5, 17, 2, 43, 3, 31} in {5 x 17, 2 x 43, 3 x 31} are the the other remaining factors of 85, 86 and 93.
Use in Mathematics: LCM of 85, 86 and 93
The below are some of the mathematical applications where lcm of 85, 86 and 93 can be used:
- to find the least number which is exactly divisible by 85, 86 and 93.
- to find the common denominators for the fractions having 85, 86 and 93 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 85, 86 and 93 helps to find the exact time when three similar and recurring 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 all the bells A, B and C toll together, if bell A tolls at 85 seconds, B tolls at 86 seconds and C tolls at 93 seconds repeatedly. The answer is that all bells A, B and C toll together at 679830 seconds for the first time, at 1359660 seconds for the second time, at 2039490 seconds for the third time and so on.
Important Notes: 85, 86 and 93 lcm
The below are the important notes to be remembered while solving the lcm of 85, 86 and 93:
- The repeated and non-repeated prime factors of 85, 86 and 93 should be multiplied to find the least common multiple of 85, 86 and 93, when solving lcm by using prime factors method.
- The results of lcm of 85, 86 and 93 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is LCM of 85, 86 and 93?
The below solved example with step by step work shows how to find what is the lcm of 85, 86 and 93 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 85, 86 and 93?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 85
B = 86
C = 93
What to be found:
Find lcm of 85, 86 and 93
step 2 Find the prime factors of 85, 86 and 93:
Prime factors of 85 = 5 x 17
Prime factors of 86 = 2 x 43
Prime factors of 93 = 3 x 31
step 3Identify the repeated and non-repeated prime factors of 85, 86 and 93:
Since there is no common factors between 85, 86 and 93, multiplying the given numbers directly provides the LCM of
85, 86 and 93.
= 85 x 86 x 93
= 679830
LCM(85, 86 and 93) = 679830
Hence,
The Least Common Multiple of 85, 86 and 93 is 679830
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 85, 86 and 93.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 85, 86 and 93
What to be found:
lcm (85, 86, 93) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
85, 86 and 93
step 3 Choose the divisor which divides each or most of the given integers (85, 86 and 93), 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, 86 and 93 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 85 | 86 | 93 |
| 3 | 85 | 43 | 93 |
| 5 | 85 | 43 | 31 |
| 17 | 17 | 43 | 31 |
| 31 | 1 | 43 | 31 |
| 43 | 1 | 43 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 85, 86 and 93:
= 2 x 3 x 5 x 17 x 31 x 43
= 679830
LCM(85, 86, 93) = 679830
The LCM of three numbers 85, 86 and 93 is 679830