LCM of 22, 42 and 57
8778 is the LCM of 22, 42 and 57. 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 22, 42 and 57, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 22, 42 and 57?
lcm (22 42 57) = (?)
22 => 2 x 11
42 => 2 x 3 x 7
57 => 3 x 19
= 2 x 3 x 11 x 7 x 19
= 8778
lcm (22, 42 and 57) = 8778
The LCM of 22, 42 and 57 is 8778
where,
22 is a positive integer,
42 is a positive integer,
8778 is the LCM of 22, 42 and 57,
{2, 3} in {2 x 11, 2 x 3 x 7, 3 x 19} are the most repeated factors of 22, 42 and 57,
{11, 7, 19} in {2 x 11, 2 x 3 x 7, 3 x 19} are the the other remaining factors of 22, 42 and 57.
Use in Mathematics: LCM of 22, 42 and 57
The below are some of the mathematical applications where lcm of 22, 42 and 57 can be used:
- to find the least number which is exactly divisible by 22, 42 and 57.
- to find the common denominators for the fractions having 22, 42 and 57 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 22, 42 and 57 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 22 seconds, B tolls at 42 seconds and C tolls at 57 seconds repeatedly. The answer is that all bells A, B and C toll together at 8778 seconds for the first time, at 17556 seconds for the second time, at 26334 seconds for the third time and so on.
Important Notes: 22, 42 and 57 lcm
The below are the important notes to be remembered while solving the lcm of 22, 42 and 57:
- The repeated and non-repeated prime factors of 22, 42 and 57 should be multiplied to find the least common multiple of 22, 42 and 57, when solving lcm by using prime factors method.
- The results of lcm of 22, 42 and 57 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 22, 42 and 57?
The below solved example with step by step work shows how to find what is the lcm of 22, 42 and 57 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 22, 42 and 57?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 22
B = 42
C = 57
What to be found:
Find lcm of 22, 42 and 57
step 2 Find the prime factors of 22, 42 and 57:
Prime factors of 22 = 2 x 11
Prime factors of 42 = 2 x 3 x 7
Prime factors of 57 = 3 x 19
step 3 Identify the repeated and non-repeated prime factors of 22, 42 and 57:
{2, 3} are the most repeated factors and {11, 7, 19} are the non-repeated factors of 22, 42 and 57.
step 4 Find the product of repeated and non-repeated prime factors of 22, 42 and 57:
= 2 x 3 x 11 x 7 x 19
= 8778
LCM(22, 42 and 57) = 8778
Hence,
The Least Common Multiple of 22, 42 and 57 is 8778
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 22, 42 and 57.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 22, 42 and 57
What to be found:
lcm (22, 42, 57) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
22, 42 and 57
step 3 Choose the divisor which divides each or most of the given integers (22, 42 and 57), 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 22, 42 and 57 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 22 | 42 | 57 |
| 3 | 11 | 21 | 57 |
| 7 | 11 | 7 | 19 |
| 11 | 11 | 1 | 19 |
| 19 | 1 | 1 | 19 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 22, 42 and 57:
= 2 x 3 x 7 x 11 x 19
= 8778
LCM(22, 42, 57) = 8778
The LCM of three numbers 22, 42 and 57 is 8778