LCM of 54, 81 and 88
7128 is the LCM of 54, 81 and 88. 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, 81 and 88, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 54, 81 and 88?
lcm (54 81 88) = (?)
54 => 2 x 3 x 3 x 3
81 => 3 x 3 x 3 x 3
88 => 2 x 2 x 2 x 11
= 2 x 3 x 3 x 3 x 3 x 2 x 2 x 11
= 7128
lcm (54, 81 and 88) = 7128
The LCM of 54, 81 and 88 is 7128
where,
54 is a positive integer,
81 is a positive integer,
7128 is the LCM of 54, 81 and 88,
{2, 3, 3, 3} in {2 x 3 x 3 x 3, 3 x 3 x 3 x 3, 2 x 2 x 2 x 11} are the most repeated factors of 54, 81 and 88,
{3, 2, 2, 11} in {2 x 3 x 3 x 3, 3 x 3 x 3 x 3, 2 x 2 x 2 x 11} are the the other remaining factors of 54, 81 and 88.
Use in Mathematics: LCM of 54, 81 and 88
The below are some of the mathematical applications where lcm of 54, 81 and 88 can be used:
- to find the least number which is exactly divisible by 54, 81 and 88.
- to find the common denominators for the fractions having 54, 81 and 88 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 54, 81 and 88 helps to find the exact time when three similar and recurring 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 all the bells A, B and C toll together, if bell A tolls at 54 seconds, B tolls at 81 seconds and C tolls at 88 seconds repeatedly. The answer is that all bells A, B and C toll together at 7128 seconds for the first time, at 14256 seconds for the second time, at 21384 seconds for the third time and so on.
Important Notes: 54, 81 and 88 lcm
The below are the important notes to be remembered while solving the lcm of 54, 81 and 88:
- The repeated and non-repeated prime factors of 54, 81 and 88 should be multiplied to find the least common multiple of 54, 81 and 88, when solving lcm by using prime factors method.
- The results of lcm of 54, 81 and 88 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is LCM of 54, 81 and 88?
The below solved example with step by step work shows how to find what is the lcm of 54, 81 and 88 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 54, 81 and 88?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 54
B = 81
C = 88
What to be found:
Find lcm of 54, 81 and 88
step 2 Find the prime factors of 54, 81 and 88:
Prime factors of 54 = 2 x 3 x 3 x 3
Prime factors of 81 = 3 x 3 x 3 x 3
Prime factors of 88 = 2 x 2 x 2 x 11
step 3 Identify the repeated and non-repeated prime factors of 54, 81 and 88:
{2, 3, 3, 3} are the most repeated factors and {3, 2, 2, 11} are the non-repeated factors of 54, 81 and 88.
step 4 Find the product of repeated and non-repeated prime factors of 54, 81 and 88:
= 2 x 3 x 3 x 3 x 3 x 2 x 2 x 11
= 7128
LCM(54, 81 and 88) = 7128
Hence,
The Least Common Multiple of 54, 81 and 88 is 7128
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 54, 81 and 88.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 54, 81 and 88
What to be found:
lcm (54, 81, 88) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
54, 81 and 88
step 3 Choose the divisor which divides each or most of the given integers (54, 81 and 88), 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, 81 and 88 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 54 | 81 | 88 |
| 2 | 27 | 81 | 44 |
| 2 | 27 | 81 | 22 |
| 3 | 27 | 81 | 11 |
| 3 | 9 | 27 | 11 |
| 3 | 3 | 9 | 11 |
| 3 | 1 | 3 | 11 |
| 11 | 1 | 1 | 11 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 54, 81 and 88:
= 2 x 2 x 2 x 3 x 3 x 3 x 3 x 11
= 7128
LCM(54, 81, 88) = 7128
The LCM of three numbers 54, 81 and 88 is 7128