LCM of 18, 21 and 44
2772 is the LCM of 18, 21 and 44. 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 18, 21 and 44, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 18, 21 and 44?
lcm (18 21 44) = (?)
18 => 2 x 3 x 3
21 => 3 x 7
44 => 2 x 2 x 11
= 2 x 3 x 3 x 7 x 2 x 11
= 2772
lcm (18, 21 and 44) = 2772
The LCM of 18, 21 and 44 is 2772
where,
18 is a positive integer,
21 is a positive integer,
2772 is the LCM of 18, 21 and 44,
{2, 3} in {2 x 3 x 3, 3 x 7, 2 x 2 x 11} are the most repeated factors of 18, 21 and 44,
{3, 7, 2, 11} in {2 x 3 x 3, 3 x 7, 2 x 2 x 11} are the the other remaining factors of 18, 21 and 44.
Use in Mathematics: LCM of 18, 21 and 44
The below are some of the mathematical applications where lcm of 18, 21 and 44 can be used:
- to find the least number which is exactly divisible by 18, 21 and 44.
- to find the common denominators for the fractions having 18, 21 and 44 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 18, 21 and 44 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 18 seconds, B tolls at 21 seconds and C tolls at 44 seconds repeatedly. The answer is that all bells A, B and C toll together at 2772 seconds for the first time, at 5544 seconds for the second time, at 8316 seconds for the third time and so on.
Important Notes: 18, 21 and 44 lcm
The below are the important notes to be remembered while solving the lcm of 18, 21 and 44:
- The repeated and non-repeated prime factors of 18, 21 and 44 should be multiplied to find the least common multiple of 18, 21 and 44, when solving lcm by using prime factors method.
- The results of lcm of 18, 21 and 44 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 18, 21 and 44?
The below solved example with step by step work shows how to find what is the lcm of 18, 21 and 44 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 18, 21 and 44?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 18
B = 21
C = 44
What to be found:
Find lcm of 18, 21 and 44
step 2 Find the prime factors of 18, 21 and 44:
Prime factors of 18 = 2 x 3 x 3
Prime factors of 21 = 3 x 7
Prime factors of 44 = 2 x 2 x 11
step 3 Identify the repeated and non-repeated prime factors of 18, 21 and 44:
{2, 3} are the most repeated factors and {3, 7, 2, 11} are the non-repeated factors of 18, 21 and 44.
step 4 Find the product of repeated and non-repeated prime factors of 18, 21 and 44:
= 2 x 3 x 3 x 7 x 2 x 11
= 2772
LCM(18, 21 and 44) = 2772
Hence,
The Least Common Multiple of 18, 21 and 44 is 2772
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 18, 21 and 44.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 18, 21 and 44
What to be found:
lcm (18, 21, 44) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
18, 21 and 44
step 3 Choose the divisor which divides each or most of the given integers (18, 21 and 44), 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 18, 21 and 44 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 18 | 21 | 44 |
| 2 | 9 | 21 | 22 |
| 3 | 9 | 21 | 11 |
| 3 | 3 | 7 | 11 |
| 7 | 1 | 7 | 11 |
| 11 | 1 | 1 | 11 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 18, 21 and 44:
= 2 x 2 x 3 x 3 x 7 x 11
= 2772
LCM(18, 21, 44) = 2772
The LCM of three numbers 18, 21 and 44 is 2772