LCM of 8, 9 and 40
360 is the LCM of 8, 9 and 40. 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 8, 9 and 40, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 8, 9 and 40?
lcm (8 9 40) = (?)
8 => 2 x 2 x 2
9 => 3 x 3
40 => 2 x 2 x 2 x 5
= 2 x 2 x 2 x 3 x 3 x 5
= 360
lcm (8, 9 and 40) = 360
The LCM of 8, 9 and 40 is 360
where,
8 is a positive integer,
9 is a positive integer,
360 is the LCM of 8, 9 and 40,
{2, 2, 2} in {2 x 2 x 2, 3 x 3, 2 x 2 x 2 x 5} are the most repeated factors of 8, 9 and 40,
{3, 3, 5} in {2 x 2 x 2, 3 x 3, 2 x 2 x 2 x 5} are the the other remaining factors of 8, 9 and 40.
Use in Mathematics: LCM of 8, 9 and 40
The below are some of the mathematical applications where lcm of 8, 9 and 40 can be used:
- to find the least number which is exactly divisible by 8, 9 and 40.
- to find the common denominators for the fractions having 8, 9 and 40 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 8, 9 and 40 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 8 seconds, B tolls at 9 seconds and C tolls at 40 seconds repeatedly. The answer is that all bells A, B and C toll together at 360 seconds for the first time, at 720 seconds for the second time, at 1080 seconds for the third time and so on.
Important Notes: 8, 9 and 40 lcm
The below are the important notes to be remembered while solving the lcm of 8, 9 and 40:
- The repeated and non-repeated prime factors of 8, 9 and 40 should be multiplied to find the least common multiple of 8, 9 and 40, when solving lcm by using prime factors method.
- The results of lcm of 8, 9 and 40 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 8, 9 and 40?
The below solved example with step by step work shows how to find what is the lcm of 8, 9 and 40 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 8, 9 and 40?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 8
B = 9
C = 40
What to be found:
Find lcm of 8, 9 and 40
step 2 Find the prime factors of 8, 9 and 40:
Prime factors of 8 = 2 x 2 x 2
Prime factors of 9 = 3 x 3
Prime factors of 40 = 2 x 2 x 2 x 5
step 3 Identify the repeated and non-repeated prime factors of 8, 9 and 40:
{2, 2, 2} are the most repeated factors and {3, 3, 5} are the non-repeated factors of 8, 9 and 40.
step 4 Find the product of repeated and non-repeated prime factors of 8, 9 and 40:
= 2 x 2 x 2 x 3 x 3 x 5
= 360
LCM(8, 9 and 40) = 360
Hence,
The Least Common Multiple of 8, 9 and 40 is 360
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 8, 9 and 40.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 8, 9 and 40
What to be found:
lcm (8, 9, 40) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
8, 9 and 40
step 3 Choose the divisor which divides each or most of the given integers (8, 9 and 40), 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 8, 9 and 40 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 8 | 9 | 40 |
| 2 | 4 | 9 | 20 |
| 2 | 2 | 9 | 10 |
| 3 | 1 | 9 | 5 |
| 3 | 1 | 3 | 5 |
| 5 | 1 | 1 | 5 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 8, 9 and 40:
= 2 x 2 x 2 x 3 x 3 x 5
= 360
LCM(8, 9, 40) = 360
The LCM of three numbers 8, 9 and 40 is 360