23, 78 and 92 LCM
LCM of 23, 78 and 92 is equal to 3588. The comprehensive work provides more insight of how to find what is the lcm of 23, 78 and 92 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 23, 78 and 92?
lcm (23 78 92) = (?)
23 => 23
78 => 2 x 3 x 13
92 => 2 x 2 x 23
= 2 x 23 x 3 x 13 x 2
= 3588
lcm (23, 78 and 92) = 3588
3588 is the lcm of 23, 78 and 92.
where,
23 is a positive integer,
78 is a positive integer,
3588 is the lcm of 23, 78 and 92,
{2, 23} in {23, 2 x 3 x 13, 2 x 2 x 23} are the most repeated factors of 23, 78 and 92,
{3, 13, 2} in {23, 2 x 3 x 13, 2 x 2 x 23} are the the other remaining factors of 23, 78 and 92.
Use in Mathematics: LCM of 23, 78 and 92
The below are some of the mathematical applications where lcm of 23, 78 and 92 can be used:
- to find the least number which is exactly divisible by 23, 78 and 92.
- to find the common denominators for the fractions having 23, 78 and 92 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 23, 78 and 92 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 23 seconds, B tolls at 78 seconds and C tolls at 92 seconds repeatedly. The answer is that all bells A, B and C toll together at 3588 seconds for the first time, at 7176 seconds for the second time, at 10764 seconds for the third time and so on.
Important Notes: 23, 78 and 92 lcm
The below are the important notes to be remembered while solving the lcm of 23, 78 and 92:
- The repeated and non-repeated prime factors of 23, 78 and 92 should be multiplied to find the least common multiple of 23, 78 and 92, when solving lcm by using prime factors method.
- The results of lcm of 23, 78 and 92 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 the LCM of 23, 78 and 92?
The below solved example with step by step work shows how to find what is the lcm of 23, 78 and 92 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 23, 78 and 92?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 23
B = 78
C = 92
What to be found:
find the lcm of 23, 78 and 92
step 2 Find the prime factors of 23, 78 and 92:
Prime factors of 23 = 23
Prime factors of 78 = 2 x 3 x 13
Prime factors of 92 = 2 x 2 x 23
step 3 Identify the repeated and non-repeated prime factors of 23, 78 and 92:
{2, 23} are the most repeated factors and {3, 13, 2} are the non-repeated factors of 23, 78 and 92.
step 4 Find the product of repeated and non-repeated prime factors of 23, 78 and 92:
= 2 x 23 x 3 x 13 x 2
= 3588
lcm(20 and 30) = 3588
Hence,
lcm of 23, 78 and 92 is 3588
This special division method is the easiest way to understand the entire calculation of what is the lcm of 23, 78 and 92.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 23, 78 and 92
What to be found:
lcm (23, 78, 92) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
23, 78 and 92
step 3 Choose the divisor which divides each or most of the given integers (23, 78 and 92), 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 23, 78 and 92 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 23 | 78 | 92 |
| 2 | 23 | 39 | 46 |
| 3 | 23 | 39 | 23 |
| 13 | 23 | 13 | 23 |
| 23 | 23 | 1 | 23 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 23, 78 and 92:
= 2 x 2 x 3 x 13 x 23
= 3588
LCM(23, 78, 92) = 3588
The least common multiple for three numbers 23, 78 and 92 is 3588