LCM of 188 and 220
10340 is the LCM of 188 and 220. 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 188 and 220, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 188 and 220?
lcm (188 220) = (?)
188 => 2 x 2 x 47
220 => 2 x 2 x 5 x 11
= 2 x 2 x 47 x 5 x 11
= 10340
lcm (188 and 220) = 10340
10340 is the LCM of 188 and 220.
where,
188 is a positive integer,
220 is a positive integer,
10340 is the LCM of 188 and 220,
{2 x 2} in {2 x 2 x 47, 2 x 2 x 5 x 11} are the common factors of 188 and 220,
{47 x 5 x 11} in {2 x 2 x 47, 2 x 2 x 5 x 11} are the uncommon factors of 188 and 220.
Use in Mathematics: LCM of 188 and 220
The below are some of the mathematical applications where lcm of 188 and 220 can be used:
- to find the least number which is exactly divisible by 188 and 220.
- to find the common denominator for two fractions having 188 and 220 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 188 and 220 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 188 seconds and bell B tolls at 220 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: 188 and 220 lcm
The below are the important notes to be remembered while solving the lcm of 188 and 220:
- The common prime factors and the remaining prime factors of 188 and 220 should be multiplied to find the least common multiple of 188 and 220, when solving lcm by using prime factors method.
- The results of lcm of 188 and 220, and the lcm of 220 and 188 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 188 and 220?
The below solved example with step by step work shows how to find what is the lcm of 188 and 220 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 188 and 220?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 188
B = 220
What to be found:
find the lcm of 188 and 220
step 2 Find the prime factors of 188 and 220:
Prime factors of 188 = 2 x 2 x 47
Prime factors of 220 = 2 x 2 x 5 x 11
step 3 Identify the repeated and non-repeated prime factors of 188 and 220:
{2, 2} are the most repeated factors and {47 x 5 x 11} are the non-repeated factors of 188 and 220.
step 4 Find the product of repeated and non-repeated prime factors of 188 and 220:
= 2 x 2 x 47 x 5 x 11
= 10340
lcm(188 and 220) = 10340
Hence,
lcm of 188 and 220 is 10340
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 188 and 220.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 188 and 220
What to be found:
lcm (188, 220) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
188 and 220
step 3 Choose the divisor which divides each or most of the given integers (188 and 220), 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 188 and 220 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 188 | 220 |
| 2 | 94 | 110 |
| 5 | 47 | 55 |
| 11 | 47 | 11 |
| 47 | 47 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 188 and 220:
= 2 x 2 x 5 x 11 x 47
= 10340
LCM(188, 220) = 10340
The LCM of two numbers 188 and 220 is 10340