LCM of 110 and 188
10340 is the LCM of 110 and 188. 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 110 and 188, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 110 and 188?
lcm (110 188) = (?)
110 => 2 x 5 x 11
188 => 2 x 2 x 47
= 2 x 5 x 11 x 2 x 47
= 10340
lcm (110 and 188) = 10340
10340 is the LCM of 110 and 188.
where,
110 is a positive integer,
188 is a positive integer,
10340 is the LCM of 110 and 188,
{2} in {2 x 5 x 11, 2 x 2 x 47} is the common factors of 110 and 188,
{5 x 11 x 2 x 47} in {2 x 5 x 11, 2 x 2 x 47} are the uncommon factors of 110 and 188.
Use in Mathematics: LCM of 110 and 188
The below are some of the mathematical applications where lcm of 110 and 188 can be used:
- to find the least number which is exactly divisible by 110 and 188.
- to find the common denominator for two fractions having 110 and 188 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 110 and 188 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 110 seconds and bell B tolls at 188 seconds repeatedly. The answer is that all bells A and B toll together at 10340 seconds for the first time, at 20680 seconds for the second time, at 31020 seconds for the third time and so on.
Important Notes: 110 and 188 lcm
The below are the important notes to be remembered while solving the lcm of 110 and 188:
- The common prime factors and the remaining prime factors of 110 and 188 should be multiplied to find the least common multiple of 110 and 188, when solving lcm by using prime factors method.
- The results of lcm of 110 and 188, and the lcm of 188 and 110 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 110 and 188?
The below solved example with step by step work shows how to find what is the lcm of 110 and 188 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 110 and 188?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 110
B = 188
What to be found:
find the lcm of 110 and 188
step 2 Find the prime factors of 110 and 188:
Prime factors of 110 = 2 x 5 x 11
Prime factors of 188 = 2 x 2 x 47
step 3 Identify the repeated and non-repeated prime factors of 110 and 188:
{2} is the most repeated factor and {5 x 11 x 2 x 47} are the non-repeated factors of 110 and 188.
step 4 Find the product of repeated and non-repeated prime factors of 110 and 188:
= 2 x 5 x 11 x 2 x 47
= 10340
lcm(110 and 188) = 10340
Hence,
lcm of 110 and 188 is 10340
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 110 and 188.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 110 and 188
What to be found:
lcm (110, 188) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
110 and 188
step 3 Choose the divisor which divides each or most of the given integers (110 and 188), 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 110 and 188 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 110 | 188 |
| 2 | 55 | 94 |
| 5 | 55 | 47 |
| 11 | 11 | 47 |
| 47 | 1 | 47 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 110 and 188:
= 2 x 2 x 5 x 11 x 47
= 10340
LCM(110, 188) = 10340
The LCM of two numbers 110 and 188 is 10340