LCM of 54, 62 and 78
21762 is the LCM of 54, 62 and 78. 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, 62 and 78, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 54, 62 and 78?
lcm (54 62 78) = (?)
54 => 2 x 3 x 3 x 3
62 => 2 x 31
78 => 2 x 3 x 13
= 2 x 3 x 3 x 3 x 31 x 13
= 21762
lcm (54, 62 and 78) = 21762
The LCM of 54, 62 and 78 is 21762
where,
54 is a positive integer,
62 is a positive integer,
21762 is the LCM of 54, 62 and 78,
{2, 3} in {2 x 3 x 3 x 3, 2 x 31, 2 x 3 x 13} are the most repeated factors of 54, 62 and 78,
{3, 3, 31, 13} in {2 x 3 x 3 x 3, 2 x 31, 2 x 3 x 13} are the the other remaining factors of 54, 62 and 78.
Use in Mathematics: LCM of 54, 62 and 78
The below are some of the mathematical applications where lcm of 54, 62 and 78 can be used:
- to find the least number which is exactly divisible by 54, 62 and 78.
- to find the common denominators for the fractions having 54, 62 and 78 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 54, 62 and 78 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 62 seconds and C tolls at 78 seconds repeatedly. The answer is that all bells A, B and C toll together at 21762 seconds for the first time, at 43524 seconds for the second time, at 65286 seconds for the third time and so on.
Important Notes: 54, 62 and 78 lcm
The below are the important notes to be remembered while solving the lcm of 54, 62 and 78:
- The repeated and non-repeated prime factors of 54, 62 and 78 should be multiplied to find the least common multiple of 54, 62 and 78, when solving lcm by using prime factors method.
- The results of lcm of 54, 62 and 78 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, 62 and 78?
The below solved example with step by step work shows how to find what is the lcm of 54, 62 and 78 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 54, 62 and 78?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 54
B = 62
C = 78
What to be found:
Find lcm of 54, 62 and 78
step 2 Find the prime factors of 54, 62 and 78:
Prime factors of 54 = 2 x 3 x 3 x 3
Prime factors of 62 = 2 x 31
Prime factors of 78 = 2 x 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 54, 62 and 78:
{2, 3} are the most repeated factors and {3, 3, 31, 13} are the non-repeated factors of 54, 62 and 78.
step 4 Find the product of repeated and non-repeated prime factors of 54, 62 and 78:
= 2 x 3 x 3 x 3 x 31 x 13
= 21762
LCM(54, 62 and 78) = 21762
Hence,
The Least Common Multiple of 54, 62 and 78 is 21762
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 54, 62 and 78.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 54, 62 and 78
What to be found:
lcm (54, 62, 78) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
54, 62 and 78
step 3 Choose the divisor which divides each or most of the given integers (54, 62 and 78), 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, 62 and 78 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 54 | 62 | 78 |
| 3 | 27 | 31 | 39 |
| 3 | 9 | 31 | 13 |
| 3 | 3 | 31 | 13 |
| 13 | 1 | 31 | 13 |
| 31 | 1 | 31 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 54, 62 and 78:
= 2 x 3 x 3 x 3 x 13 x 31
= 21762
LCM(54, 62, 78) = 21762
The LCM of three numbers 54, 62 and 78 is 21762