LCM of 106 and 187
19822 is the LCM of 106 and 187. 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 106 and 187, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 106 and 187?
lcm (106 187) = (?)
106 => 2 x 53
187 => 11 x 17
= 2 x 53 x 11 x 17
= 19822
lcm (106 and 187) = 19822
19822 is the LCM of 106 and 187.
where,
106 is a positive integer,
187 is a positive integer,
19822 is the LCM of 106 and 187,
There is no common factors of 106 and 187 in {2 x 53, 11 x 17},
{2 x 53 x 11 x 17} in {2 x 53, 11 x 17} are the uncommon factors of 106 and 187.
Use in Mathematics: LCM of 106 and 187
The below are some of the mathematical applications where lcm of 106 and 187 can be used:
- to find the least number which is exactly divisible by 106 and 187.
- to find the common denominator for two fractions having 106 and 187 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 106 and 187 helps to find the exact time when two similar and recurring events 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 the bells A and B all toll together, if bell A tolls at 106 seconds and bell B tolls at 187 seconds repeatedly. The answer is that all bells A and B toll together at 19822 seconds for the first time, at 39644 seconds for the second time, at 59466 seconds for the third time and so on.
Important Notes: 106 and 187 lcm
The below are the important notes to be remembered while solving the lcm of 106 and 187:
- The common prime factors and the remaining prime factors of 106 and 187 should be multiplied to find the least common multiple of 106 and 187, when solving lcm by using prime factors method.
- The results of lcm of 106 and 187, and the lcm of 187 and 106 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 106 and 187?
The below solved example with step by step work shows how to find what is the lcm of 106 and 187 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 106 and 187?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 106
B = 187
What to be found:
find the lcm of 106 and 187
step 2 Find the prime factors of 106 and 187:
Prime factors of 106 = 2 x 53
Prime factors of 187 = 11 x 17
step 3Identify the repeated and non-repeated prime factors of 106 and 187:
Since there is no common factors between 106 and 187, multiplying the given numbers directly provides the LCM of
106 and 187.
= 106 x 187
= 19822
lcm(106 and 187) = 19822
Hence,
lcm of 106 and 187 is 19822
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 106 and 187.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 106 and 187
What to be found:
lcm (106, 187) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
106 and 187
step 3 Choose the divisor which divides each or most of the given integers (106 and 187), 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 106 and 187 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 106 | 187 |
| 11 | 53 | 187 |
| 17 | 53 | 17 |
| 53 | 53 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 106 and 187:
= 2 x 11 x 17 x 53
= 19822
LCM(106, 187) = 19822
The LCM of two numbers 106 and 187 is 19822