LCM of 114 and 278
15846 is the LCM of 114 and 278. 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 114 and 278, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 114 and 278?
lcm (114 278) = (?)
114 => 2 x 3 x 19
278 => 2 x 139
= 2 x 3 x 19 x 139
= 15846
lcm (114 and 278) = 15846
15846 is the LCM of 114 and 278.
where,
114 is a positive integer,
278 is a positive integer,
15846 is the LCM of 114 and 278,
{2} in {2 x 3 x 19, 2 x 139} is the common factors of 114 and 278,
{3 x 19 x 139} in {2 x 3 x 19, 2 x 139} are the uncommon factors of 114 and 278.
Use in Mathematics: LCM of 114 and 278
The below are some of the mathematical applications where lcm of 114 and 278 can be used:
- to find the least number which is exactly divisible by 114 and 278.
- to find the common denominator for two fractions having 114 and 278 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 114 and 278 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 114 seconds and bell B tolls at 278 seconds repeatedly. The answer is that all bells A and B toll together at 15846 seconds for the first time, at 31692 seconds for the second time, at 47538 seconds for the third time and so on.
Important Notes: 114 and 278 lcm
The below are the important notes to be remembered while solving the lcm of 114 and 278:
- The common prime factors and the remaining prime factors of 114 and 278 should be multiplied to find the least common multiple of 114 and 278, when solving lcm by using prime factors method.
- The results of lcm of 114 and 278, and the lcm of 278 and 114 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 114 and 278?
The below solved example with step by step work shows how to find what is the lcm of 114 and 278 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 114 and 278?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 114
B = 278
What to be found:
find the lcm of 114 and 278
step 2 Find the prime factors of 114 and 278:
Prime factors of 114 = 2 x 3 x 19
Prime factors of 278 = 2 x 139
step 3 Identify the repeated and non-repeated prime factors of 114 and 278:
{2} is the most repeated factor and {3 x 19 x 139} are the non-repeated factors of 114 and 278.
step 4 Find the product of repeated and non-repeated prime factors of 114 and 278:
= 2 x 3 x 19 x 139
= 15846
lcm(114 and 278) = 15846
Hence,
lcm of 114 and 278 is 15846
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 114 and 278.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 114 and 278
What to be found:
lcm (114, 278) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
114 and 278
step 3 Choose the divisor which divides each or most of the given integers (114 and 278), 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 114 and 278 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 114 | 278 |
| 3 | 57 | 139 |
| 19 | 19 | 139 |
| 139 | 1 | 139 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 114 and 278:
= 2 x 3 x 19 x 139
= 15846
LCM(114, 278) = 15846
The LCM of two numbers 114 and 278 is 15846