LCM of 240 and 279
22320 is the LCM of 240 and 279. 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 240 and 279, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 240 and 279?
lcm (240 279) = (?)
240 => 2 x 2 x 2 x 2 x 3 x 5
279 => 3 x 3 x 31
= 3 x 2 x 2 x 2 x 2 x 5 x 3 x 31
= 22320
lcm (240 and 279) = 22320
22320 is the LCM of 240 and 279.
where,
240 is a positive integer,
279 is a positive integer,
22320 is the LCM of 240 and 279,
{3} in {2 x 2 x 2 x 2 x 3 x 5, 3 x 3 x 31} is the common factors of 240 and 279,
{2 x 2 x 2 x 2 x 5 x 3 x 31} in {2 x 2 x 2 x 2 x 3 x 5, 3 x 3 x 31} are the uncommon factors of 240 and 279.
Use in Mathematics: LCM of 240 and 279
The below are some of the mathematical applications where lcm of 240 and 279 can be used:
- to find the least number which is exactly divisible by 240 and 279.
- to find the common denominator for two fractions having 240 and 279 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 240 and 279 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 240 seconds and bell B tolls at 279 seconds repeatedly. The answer is that all bells A and B toll together at 22320 seconds for the first time, at 44640 seconds for the second time, at 66960 seconds for the third time and so on.
Important Notes: 240 and 279 lcm
The below are the important notes to be remembered while solving the lcm of 240 and 279:
- The common prime factors and the remaining prime factors of 240 and 279 should be multiplied to find the least common multiple of 240 and 279, when solving lcm by using prime factors method.
- The results of lcm of 240 and 279, and the lcm of 279 and 240 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 240 and 279?
The below solved example with step by step work shows how to find what is the lcm of 240 and 279 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 240 and 279?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 240
B = 279
What to be found:
find the lcm of 240 and 279
step 2 Find the prime factors of 240 and 279:
Prime factors of 240 = 2 x 2 x 2 x 2 x 3 x 5
Prime factors of 279 = 3 x 3 x 31
step 3 Identify the repeated and non-repeated prime factors of 240 and 279:
{3} is the most repeated factor and {2 x 2 x 2 x 2 x 5 x 3 x 31} are the non-repeated factors of 240 and 279.
step 4 Find the product of repeated and non-repeated prime factors of 240 and 279:
= 3 x 2 x 2 x 2 x 2 x 5 x 3 x 31
= 22320
lcm(240 and 279) = 22320
Hence,
lcm of 240 and 279 is 22320
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 240 and 279.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 240 and 279
What to be found:
lcm (240, 279) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
240 and 279
step 3 Choose the divisor which divides each or most of the given integers (240 and 279), 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 240 and 279 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 240 | 279 |
| 2 | 120 | 279 |
| 2 | 60 | 279 |
| 2 | 30 | 279 |
| 3 | 15 | 279 |
| 3 | 5 | 93 |
| 5 | 5 | 31 |
| 31 | 1 | 31 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 240 and 279:
= 2 x 2 x 2 x 2 x 3 x 3 x 5 x 31
= 22320
LCM(240, 279) = 22320
The LCM of two numbers 240 and 279 is 22320