LCM of 278 and 288
40032 is the LCM of 278 and 288. 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 278 and 288, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 278 and 288?
lcm (278 288) = (?)
278 => 2 x 139
288 => 2 x 2 x 2 x 2 x 2 x 3 x 3
= 2 x 139 x 2 x 2 x 2 x 2 x 3 x 3
= 40032
lcm (278 and 288) = 40032
40032 is the LCM of 278 and 288.
where,
278 is a positive integer,
288 is a positive integer,
40032 is the LCM of 278 and 288,
{2} in {2 x 139, 2 x 2 x 2 x 2 x 2 x 3 x 3} is the common factors of 278 and 288,
{139 x 2 x 2 x 2 x 2 x 3 x 3} in {2 x 139, 2 x 2 x 2 x 2 x 2 x 3 x 3} are the uncommon factors of 278 and 288.
Use in Mathematics: LCM of 278 and 288
The below are some of the mathematical applications where lcm of 278 and 288 can be used:
- to find the least number which is exactly divisible by 278 and 288.
- to find the common denominator for two fractions having 278 and 288 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 278 and 288 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 278 seconds and bell B tolls at 288 seconds repeatedly. The answer is that all bells A and B toll together at 40032 seconds for the first time, at 80064 seconds for the second time, at 120096 seconds for the third time and so on.
Important Notes: 278 and 288 lcm
The below are the important notes to be remembered while solving the lcm of 278 and 288:
- The common prime factors and the remaining prime factors of 278 and 288 should be multiplied to find the least common multiple of 278 and 288, when solving lcm by using prime factors method.
- The results of lcm of 278 and 288, and the lcm of 288 and 278 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 278 and 288?
The below solved example with step by step work shows how to find what is the lcm of 278 and 288 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 278 and 288?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 278
B = 288
What to be found:
find the lcm of 278 and 288
step 2 Find the prime factors of 278 and 288:
Prime factors of 278 = 2 x 139
Prime factors of 288 = 2 x 2 x 2 x 2 x 2 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 278 and 288:
{2} is the most repeated factor and {139 x 2 x 2 x 2 x 2 x 3 x 3} are the non-repeated factors of 278 and 288.
step 4 Find the product of repeated and non-repeated prime factors of 278 and 288:
= 2 x 139 x 2 x 2 x 2 x 2 x 3 x 3
= 40032
lcm(278 and 288) = 40032
Hence,
lcm of 278 and 288 is 40032
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 278 and 288.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 278 and 288
What to be found:
lcm (278, 288) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
278 and 288
step 3 Choose the divisor which divides each or most of the given integers (278 and 288), 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 278 and 288 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 278 | 288 |
| 2 | 139 | 144 |
| 2 | 139 | 72 |
| 2 | 139 | 36 |
| 2 | 139 | 18 |
| 3 | 139 | 9 |
| 3 | 139 | 3 |
| 139 | 139 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 278 and 288:
= 2 x 2 x 2 x 2 x 2 x 3 x 3 x 139
= 40032
LCM(278, 288) = 40032
The LCM of two numbers 278 and 288 is 40032