LCM of 109 and 112
12208 is the LCM of 109 and 112. 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 109 and 112, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 109 and 112?
lcm (109 112) = (?)
109 => 109
112 => 2 x 2 x 2 x 2 x 7
= 109 x 2 x 2 x 2 x 2 x 7
= 12208
lcm (109 and 112) = 12208
12208 is the LCM of 109 and 112.
where,
109 is a positive integer,
112 is a positive integer,
12208 is the LCM of 109 and 112,
There is no common factors of 109 and 112 in {109, 2 x 2 x 2 x 2 x 7},
{109 x 2 x 2 x 2 x 2 x 7} in {109, 2 x 2 x 2 x 2 x 7} are the uncommon factors of 109 and 112.
Use in Mathematics: LCM of 109 and 112
The below are some of the mathematical applications where lcm of 109 and 112 can be used:
- to find the least number which is exactly divisible by 109 and 112.
- to find the common denominator for two fractions having 109 and 112 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 109 and 112 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 109 seconds and bell B tolls at 112 seconds repeatedly. The answer is that all bells A and B toll together at 12208 seconds for the first time, at 24416 seconds for the second time, at 36624 seconds for the third time and so on.
Important Notes: 109 and 112 lcm
The below are the important notes to be remembered while solving the lcm of 109 and 112:
- The common prime factors and the remaining prime factors of 109 and 112 should be multiplied to find the least common multiple of 109 and 112, when solving lcm by using prime factors method.
- The results of lcm of 109 and 112, and the lcm of 112 and 109 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 109 and 112?
The below solved example with step by step work shows how to find what is the lcm of 109 and 112 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 109 and 112?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 109
B = 112
What to be found:
find the lcm of 109 and 112
step 2 Find the prime factors of 109 and 112:
Prime factors of 109 = 109
Prime factors of 112 = 2 x 2 x 2 x 2 x 7
step 3Identify the repeated and non-repeated prime factors of 109 and 112:
Since there is no common factors between 109 and 112, multiplying the given numbers directly provides the LCM of
109 and 112.
= 109 x 112
= 12208
lcm(109 and 112) = 12208
Hence,
lcm of 109 and 112 is 12208
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 109 and 112.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 109 and 112
What to be found:
lcm (109, 112) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
109 and 112
step 3 Choose the divisor which divides each or most of the given integers (109 and 112), 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 109 and 112 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 109 | 112 |
| 2 | 109 | 56 |
| 2 | 109 | 28 |
| 2 | 109 | 14 |
| 7 | 109 | 7 |
| 109 | 109 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 109 and 112:
= 2 x 2 x 2 x 2 x 7 x 109
= 12208
LCM(109, 112) = 12208
The LCM of two numbers 109 and 112 is 12208