LCM of 54 and 228
2052 is the LCM of 54 and 228. 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 54 and 228, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 54 and 228?
lcm (54 228) = (?)
54 => 2 x 3 x 3 x 3
228 => 2 x 2 x 3 x 19
= 2 x 3 x 3 x 3 x 2 x 19
= 2052
lcm (54 and 228) = 2052
2052 is the LCM of 54 and 228.
where,
54 is a positive integer,
228 is a positive integer,
2052 is the LCM of 54 and 228,
{2 x 3} in {2 x 3 x 3 x 3, 2 x 2 x 3 x 19} are the common factors of 54 and 228,
{3 x 3 x 2 x 19} in {2 x 3 x 3 x 3, 2 x 2 x 3 x 19} are the uncommon factors of 54 and 228.
Use in Mathematics: LCM of 54 and 228
The below are some of the mathematical applications where lcm of 54 and 228 can be used:
- to find the least number which is exactly divisible by 54 and 228.
- to find the common denominator for two fractions having 54 and 228 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 54 and 228 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 54 seconds and bell B tolls at 228 seconds repeatedly. The answer is that all bells A and B toll together at 2052 seconds for the first time, at 4104 seconds for the second time, at 6156 seconds for the third time and so on.
Important Notes: 54 and 228 lcm
The below are the important notes to be remembered while solving the lcm of 54 and 228:
- The common prime factors and the remaining prime factors of 54 and 228 should be multiplied to find the least common multiple of 54 and 228, when solving lcm by using prime factors method.
- The results of lcm of 54 and 228, and the lcm of 228 and 54 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 54 and 228?
The below solved example with step by step work shows how to find what is the lcm of 54 and 228 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 54 and 228?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 54
B = 228
What to be found:
find the lcm of 54 and 228
step 2 Find the prime factors of 54 and 228:
Prime factors of 54 = 2 x 3 x 3 x 3
Prime factors of 228 = 2 x 2 x 3 x 19
step 3 Identify the repeated and non-repeated prime factors of 54 and 228:
{2, 3} are the most repeated factors and {3 x 3 x 2 x 19} are the non-repeated factors of 54 and 228.
step 4 Find the product of repeated and non-repeated prime factors of 54 and 228:
= 2 x 3 x 3 x 3 x 2 x 19
= 2052
lcm(54 and 228) = 2052
Hence,
lcm of 54 and 228 is 2052
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 54 and 228.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 54 and 228
What to be found:
lcm (54, 228) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
54 and 228
step 3 Choose the divisor which divides each or most of the given integers (54 and 228), 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 54 and 228 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 54 | 228 |
| 2 | 27 | 114 |
| 3 | 27 | 57 |
| 3 | 9 | 19 |
| 3 | 3 | 19 |
| 19 | 1 | 19 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 54 and 228:
= 2 x 2 x 3 x 3 x 3 x 19
= 2052
LCM(54, 228) = 2052
The LCM of two numbers 54 and 228 is 2052