LCM of 26, 28 and 33
12012 is the LCM of 26, 28 and 33. 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 26, 28 and 33, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 26, 28 and 33?
lcm (26 28 33) = (?)
26 => 2 x 13
28 => 2 x 2 x 7
33 => 3 x 11
= 2 x 13 x 2 x 7 x 3 x 11
= 12012
lcm (26, 28 and 33) = 12012
The LCM of 26, 28 and 33 is 12012
where,
26 is a positive integer,
28 is a positive integer,
12012 is the LCM of 26, 28 and 33,
{2} in {2 x 13, 2 x 2 x 7, 3 x 11} is the most repeated factors of 26, 28 and 33,
{13, 2, 7, 3, 11} in {2 x 13, 2 x 2 x 7, 3 x 11} are the the other remaining factors of 26, 28 and 33.
Use in Mathematics: LCM of 26, 28 and 33
The below are some of the mathematical applications where lcm of 26, 28 and 33 can be used:
- to find the least number which is exactly divisible by 26, 28 and 33.
- to find the common denominators for the fractions having 26, 28 and 33 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 26, 28 and 33 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 26 seconds, B tolls at 28 seconds and C tolls at 33 seconds repeatedly. The answer is that all bells A, B and C toll together at 12012 seconds for the first time, at 24024 seconds for the second time, at 36036 seconds for the third time and so on.
Important Notes: 26, 28 and 33 lcm
The below are the important notes to be remembered while solving the lcm of 26, 28 and 33:
- The repeated and non-repeated prime factors of 26, 28 and 33 should be multiplied to find the least common multiple of 26, 28 and 33, when solving lcm by using prime factors method.
- The results of lcm of 26, 28 and 33 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 26, 28 and 33?
The below solved example with step by step work shows how to find what is the lcm of 26, 28 and 33 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 26, 28 and 33?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 26
B = 28
C = 33
What to be found:
Find lcm of 26, 28 and 33
step 2 Find the prime factors of 26, 28 and 33:
Prime factors of 26 = 2 x 13
Prime factors of 28 = 2 x 2 x 7
Prime factors of 33 = 3 x 11
step 3 Identify the repeated and non-repeated prime factors of 26, 28 and 33:
{2} is the most repeated factor and {13, 2, 7, 3, 11} are the non-repeated factors of 26, 28 and 33.
step 4 Find the product of repeated and non-repeated prime factors of 26, 28 and 33:
= 2 x 13 x 2 x 7 x 3 x 11
= 12012
LCM(26, 28 and 33) = 12012
Hence,
The Least Common Multiple of 26, 28 and 33 is 12012
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 26, 28 and 33.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 26, 28 and 33
What to be found:
lcm (26, 28, 33) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
26, 28 and 33
step 3 Choose the divisor which divides each or most of the given integers (26, 28 and 33), 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 26, 28 and 33 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 26 | 28 | 33 |
| 2 | 13 | 14 | 33 |
| 3 | 13 | 7 | 33 |
| 7 | 13 | 7 | 11 |
| 11 | 13 | 1 | 11 |
| 13 | 13 | 1 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 26, 28 and 33:
= 2 x 2 x 3 x 7 x 11 x 13
= 12012
LCM(26, 28, 33) = 12012
The LCM of three numbers 26, 28 and 33 is 12012