LCM of 40 and 81
3240 is the LCM of 40 and 81. 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 40 and 81, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 40 and 81?
lcm (40 81) = (?)
40 => 2 x 2 x 2 x 5
81 => 3 x 3 x 3 x 3
= 2 x 2 x 2 x 5 x 3 x 3 x 3 x 3
= 3240
lcm (40 and 81) = 3240
3240 is the LCM of 40 and 81.
where,
40 is a positive integer,
81 is a positive integer,
3240 is the LCM of 40 and 81,
There is no common factors of 40 and 81 in {2 x 2 x 2 x 5, 3 x 3 x 3 x 3},
{2 x 2 x 2 x 5 x 3 x 3 x 3 x 3} in {2 x 2 x 2 x 5, 3 x 3 x 3 x 3} are the uncommon factors of 40 and 81.
Use in Mathematics: LCM of 40 and 81
The below are some of the mathematical applications where lcm of 40 and 81 can be used:
- to find the least number which is exactly divisible by 40 and 81.
- to find the common denominator for two fractions having 40 and 81 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 40 and 81 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 40 seconds and bell B tolls at 81 seconds repeatedly. The answer is that all bells A and B toll together at 3240 seconds for the first time, at 6480 seconds for the second time, at 9720 seconds for the third time and so on.
Important Notes: 40 and 81 lcm
The below are the important notes to be remembered while solving the lcm of 40 and 81:
- The common prime factors and the remaining prime factors of 40 and 81 should be multiplied to find the least common multiple of 40 and 81, when solving lcm by using prime factors method.
- The results of lcm of 40 and 81, and the lcm of 81 and 40 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 40 and 81?
The below solved example with step by step work shows how to find what is the lcm of 40 and 81 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 40 and 81?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 40
B = 81
What to be found:
find the lcm of 40 and 81
step 2 Find the prime factors of 40 and 81:
Prime factors of 40 = 2 x 2 x 2 x 5
Prime factors of 81 = 3 x 3 x 3 x 3
step 3Identify the repeated and non-repeated prime factors of 40 and 81:
Since there is no common factors between 40 and 81, multiplying the given numbers directly provides the LCM of
40 and 81.
= 40 x 81
= 3240
lcm(40 and 81) = 3240
Hence,
lcm of 40 and 81 is 3240
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 40 and 81.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 40 and 81
What to be found:
lcm (40, 81) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
40 and 81
step 3 Choose the divisor which divides each or most of the given integers (40 and 81), 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 40 and 81 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 40 | 81 |
| 2 | 20 | 81 |
| 2 | 10 | 81 |
| 3 | 5 | 81 |
| 3 | 5 | 27 |
| 3 | 5 | 9 |
| 3 | 5 | 3 |
| 5 | 5 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 40 and 81:
= 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5
= 3240
LCM(40, 81) = 3240
The LCM of two numbers 40 and 81 is 3240