LCM of 112, 168 and 266
6384 is the LCM of 112, 168 and 266. 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 112, 168 and 266, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 112, 168 and 266?
lcm (112 168 266) = (?)
112 => 2 x 2 x 2 x 2 x 7
168 => 2 x 2 x 2 x 3 x 7
266 => 2 x 7 x 19
= 2 x 2 x 2 x 7 x 2 x 3 x 19
= 6384
lcm (112, 168 and 266) = 6384
The LCM of 112, 168 and 266 is 6384
where,
112 is a positive integer,
168 is a positive integer,
6384 is the LCM of 112, 168 and 266,
{2, 2, 2, 7} in {2 x 2 x 2 x 2 x 7, 2 x 2 x 2 x 3 x 7, 2 x 7 x 19} are the most repeated factors of 112, 168 and 266,
{2, 3, 19} in {2 x 2 x 2 x 2 x 7, 2 x 2 x 2 x 3 x 7, 2 x 7 x 19} are the the other remaining factors of 112, 168 and 266.
Use in Mathematics: LCM of 112, 168 and 266
The below are some of the mathematical applications where lcm of 112, 168 and 266 can be used:
- to find the least number which is exactly divisible by 112, 168 and 266.
- to find the common denominators for the fractions having 112, 168 and 266 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 112, 168 and 266 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 112 seconds, B tolls at 168 seconds and C tolls at 266 seconds repeatedly. The answer is that all bells A, B and C toll together at 6384 seconds for the first time, at 12768 seconds for the second time, at 19152 seconds for the third time and so on.
Important Notes: 112, 168 and 266 lcm
The below are the important notes to be remembered while solving the lcm of 112, 168 and 266:
- The repeated and non-repeated prime factors of 112, 168 and 266 should be multiplied to find the least common multiple of 112, 168 and 266, when solving lcm by using prime factors method.
- The results of lcm of 112, 168 and 266 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 112, 168 and 266?
The below solved example with step by step work shows how to find what is the lcm of 112, 168 and 266 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 112, 168 and 266?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 112
B = 168
C = 266
What to be found:
Find lcm of 112, 168 and 266
step 2 Find the prime factors of 112, 168 and 266:
Prime factors of 112 = 2 x 2 x 2 x 2 x 7
Prime factors of 168 = 2 x 2 x 2 x 3 x 7
Prime factors of 266 = 2 x 7 x 19
step 3 Identify the repeated and non-repeated prime factors of 112, 168 and 266:
{2, 2, 2, 7} are the most repeated factors and {2, 3, 19} are the non-repeated factors of 112, 168 and 266.
step 4 Find the product of repeated and non-repeated prime factors of 112, 168 and 266:
= 2 x 2 x 2 x 7 x 2 x 3 x 19
= 6384
LCM(112, 168 and 266) = 6384
Hence,
The Least Common Multiple of 112, 168 and 266 is 6384
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 112, 168 and 266.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 112, 168 and 266
What to be found:
lcm (112, 168, 266) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
112, 168 and 266
step 3 Choose the divisor which divides each or most of the given integers (112, 168 and 266), 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 112, 168 and 266 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 112 | 168 | 266 |
| 2 | 56 | 84 | 133 |
| 2 | 28 | 42 | 133 |
| 2 | 14 | 21 | 133 |
| 3 | 7 | 21 | 133 |
| 7 | 7 | 7 | 133 |
| 19 | 1 | 1 | 19 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 112, 168 and 266:
= 2 x 2 x 2 x 2 x 3 x 7 x 19
= 6384
LCM(112, 168, 266) = 6384
The LCM of three numbers 112, 168 and 266 is 6384