LCM of 224 and 254
28448 is the LCM of 224 and 254. 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 224 and 254, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 224 and 254?
lcm (224 254) = (?)
224 => 2 x 2 x 2 x 2 x 2 x 7
254 => 2 x 127
= 2 x 2 x 2 x 2 x 2 x 7 x 127
= 28448
lcm (224 and 254) = 28448
28448 is the LCM of 224 and 254.
where,
224 is a positive integer,
254 is a positive integer,
28448 is the LCM of 224 and 254,
{2} in {2 x 2 x 2 x 2 x 2 x 7, 2 x 127} is the common factors of 224 and 254,
{2 x 2 x 2 x 2 x 7 x 127} in {2 x 2 x 2 x 2 x 2 x 7, 2 x 127} are the uncommon factors of 224 and 254.
Use in Mathematics: LCM of 224 and 254
The below are some of the mathematical applications where lcm of 224 and 254 can be used:
- to find the least number which is exactly divisible by 224 and 254.
- to find the common denominator for two fractions having 224 and 254 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 224 and 254 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 224 seconds and bell B tolls at 254 seconds repeatedly. The answer is that all bells A and B toll together at 28448 seconds for the first time, at 56896 seconds for the second time, at 85344 seconds for the third time and so on.
Important Notes: 224 and 254 lcm
The below are the important notes to be remembered while solving the lcm of 224 and 254:
- The common prime factors and the remaining prime factors of 224 and 254 should be multiplied to find the least common multiple of 224 and 254, when solving lcm by using prime factors method.
- The results of lcm of 224 and 254, and the lcm of 254 and 224 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 224 and 254?
The below solved example with step by step work shows how to find what is the lcm of 224 and 254 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 224 and 254?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 224
B = 254
What to be found:
find the lcm of 224 and 254
step 2 Find the prime factors of 224 and 254:
Prime factors of 224 = 2 x 2 x 2 x 2 x 2 x 7
Prime factors of 254 = 2 x 127
step 3 Identify the repeated and non-repeated prime factors of 224 and 254:
{2} is the most repeated factor and {2 x 2 x 2 x 2 x 7 x 127} are the non-repeated factors of 224 and 254.
step 4 Find the product of repeated and non-repeated prime factors of 224 and 254:
= 2 x 2 x 2 x 2 x 2 x 7 x 127
= 28448
lcm(224 and 254) = 28448
Hence,
lcm of 224 and 254 is 28448
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 224 and 254.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 224 and 254
What to be found:
lcm (224, 254) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
224 and 254
step 3 Choose the divisor which divides each or most of the given integers (224 and 254), 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 224 and 254 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 224 | 254 |
| 2 | 112 | 127 |
| 2 | 56 | 127 |
| 2 | 28 | 127 |
| 2 | 14 | 127 |
| 7 | 7 | 127 |
| 127 | 1 | 127 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 224 and 254:
= 2 x 2 x 2 x 2 x 2 x 7 x 127
= 28448
LCM(224, 254) = 28448
The LCM of two numbers 224 and 254 is 28448