LCM of 6 and 240
240 is the LCM of 6 and 240. 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 6 and 240, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 6 and 240?
lcm (6 240) = (?)
6 => 2 x 3
240 => 2 x 2 x 2 x 2 x 3 x 5
= 2 x 3 x 2 x 2 x 2 x 5
= 240
lcm (6 and 240) = 240
240 is the LCM of 6 and 240.
where,
6 is a positive integer,
240 is a positive integer,
240 is the LCM of 6 and 240,
{2 x 3} in {2 x 3, 2 x 2 x 2 x 2 x 3 x 5} are the common factors of 6 and 240,
{2 x 2 x 2 x 5} in {2 x 3, 2 x 2 x 2 x 2 x 3 x 5} are the uncommon factors of 6 and 240.
Use in Mathematics: LCM of 6 and 240
The below are some of the mathematical applications where lcm of 6 and 240 can be used:
- to find the least number which is exactly divisible by 6 and 240.
- to find the common denominator for two fractions having 6 and 240 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 6 and 240 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 6 seconds and bell B tolls at 240 seconds repeatedly. The answer is that all bells A and B toll together at 240 seconds for the first time, at 480 seconds for the second time, at 720 seconds for the third time and so on.
Important Notes: 6 and 240 lcm
The below are the important notes to be remembered while solving the lcm of 6 and 240:
- The common prime factors and the remaining prime factors of 6 and 240 should be multiplied to find the least common multiple of 6 and 240, when solving lcm by using prime factors method.
- The results of lcm of 6 and 240, and the lcm of 240 and 6 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 6 and 240?
The below solved example with step by step work shows how to find what is the lcm of 6 and 240 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 6 and 240?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 6
B = 240
What to be found:
find the lcm of 6 and 240
step 2 Find the prime factors of 6 and 240:
Prime factors of 6 = 2 x 3
Prime factors of 240 = 2 x 2 x 2 x 2 x 3 x 5
step 3 Identify the repeated and non-repeated prime factors of 6 and 240:
{2, 3} are the most repeated factors and {2 x 2 x 2 x 5} are the non-repeated factors of 6 and 240.
step 4 Find the product of repeated and non-repeated prime factors of 6 and 240:
= 2 x 3 x 2 x 2 x 2 x 5
= 240
lcm(6 and 240) = 240
Hence,
lcm of 6 and 240 is 240
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 6 and 240.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 6 and 240
What to be found:
lcm (6, 240) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
6 and 240
step 3 Choose the divisor which divides each or most of the given integers (6 and 240), 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 6 and 240 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 6 | 240 |
| 2 | 3 | 120 |
| 2 | 3 | 60 |
| 2 | 3 | 30 |
| 3 | 3 | 15 |
| 5 | 1 | 5 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 6 and 240:
= 2 x 2 x 2 x 2 x 3 x 5
= 240
LCM(6, 240) = 240
The LCM of two numbers 6 and 240 is 240