LCM of 40 and 285
2280 is the LCM of 40 and 285. 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 285, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 40 and 285?
lcm (40 285) = (?)
40 => 2 x 2 x 2 x 5
285 => 3 x 5 x 19
= 5 x 2 x 2 x 2 x 3 x 19
= 2280
lcm (40 and 285) = 2280
2280 is the LCM of 40 and 285.
where,
40 is a positive integer,
285 is a positive integer,
2280 is the LCM of 40 and 285,
{5} in {2 x 2 x 2 x 5, 3 x 5 x 19} is the common factors of 40 and 285,
{2 x 2 x 2 x 3 x 19} in {2 x 2 x 2 x 5, 3 x 5 x 19} are the uncommon factors of 40 and 285.
Use in Mathematics: LCM of 40 and 285
The below are some of the mathematical applications where lcm of 40 and 285 can be used:
- to find the least number which is exactly divisible by 40 and 285.
- to find the common denominator for two fractions having 40 and 285 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 40 and 285 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 285 seconds repeatedly. The answer is that all bells A and B toll together at 2280 seconds for the first time, at 4560 seconds for the second time, at 6840 seconds for the third time and so on.
Important Notes: 40 and 285 lcm
The below are the important notes to be remembered while solving the lcm of 40 and 285:
- The common prime factors and the remaining prime factors of 40 and 285 should be multiplied to find the least common multiple of 40 and 285, when solving lcm by using prime factors method.
- The results of lcm of 40 and 285, and the lcm of 285 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 285?
The below solved example with step by step work shows how to find what is the lcm of 40 and 285 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 40 and 285?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 40
B = 285
What to be found:
find the lcm of 40 and 285
step 2 Find the prime factors of 40 and 285:
Prime factors of 40 = 2 x 2 x 2 x 5
Prime factors of 285 = 3 x 5 x 19
step 3 Identify the repeated and non-repeated prime factors of 40 and 285:
{5} is the most repeated factor and {2 x 2 x 2 x 3 x 19} are the non-repeated factors of 40 and 285.
step 4 Find the product of repeated and non-repeated prime factors of 40 and 285:
= 5 x 2 x 2 x 2 x 3 x 19
= 2280
lcm(40 and 285) = 2280
Hence,
lcm of 40 and 285 is 2280
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 40 and 285.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 40 and 285
What to be found:
lcm (40, 285) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
40 and 285
step 3 Choose the divisor which divides each or most of the given integers (40 and 285), 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 285 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 40 | 285 |
| 2 | 20 | 285 |
| 2 | 10 | 285 |
| 3 | 5 | 285 |
| 5 | 5 | 95 |
| 19 | 1 | 19 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 40 and 285:
= 2 x 2 x 2 x 3 x 5 x 19
= 2280
LCM(40, 285) = 2280
The LCM of two numbers 40 and 285 is 2280