LCM of 109 and 224
24416 is the LCM of 109 and 224. 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 224, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 109 and 224?
lcm (109 224) = (?)
109 => 109
224 => 2 x 2 x 2 x 2 x 2 x 7
= 109 x 2 x 2 x 2 x 2 x 2 x 7
= 24416
lcm (109 and 224) = 24416
24416 is the LCM of 109 and 224.
where,
109 is a positive integer,
224 is a positive integer,
24416 is the LCM of 109 and 224,
There is no common factors of 109 and 224 in {109, 2 x 2 x 2 x 2 x 2 x 7},
{109 x 2 x 2 x 2 x 2 x 2 x 7} in {109, 2 x 2 x 2 x 2 x 2 x 7} are the uncommon factors of 109 and 224.
Use in Mathematics: LCM of 109 and 224
The below are some of the mathematical applications where lcm of 109 and 224 can be used:
- to find the least number which is exactly divisible by 109 and 224.
- to find the common denominator for two fractions having 109 and 224 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 109 and 224 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 224 seconds repeatedly. The answer is that all bells A and B toll together at 24416 seconds for the first time, at 48832 seconds for the second time, at 73248 seconds for the third time and so on.
Important Notes: 109 and 224 lcm
The below are the important notes to be remembered while solving the lcm of 109 and 224:
- The common prime factors and the remaining prime factors of 109 and 224 should be multiplied to find the least common multiple of 109 and 224, when solving lcm by using prime factors method.
- The results of lcm of 109 and 224, and the lcm of 224 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 224?
The below solved example with step by step work shows how to find what is the lcm of 109 and 224 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 109 and 224?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 109
B = 224
What to be found:
find the lcm of 109 and 224
step 2 Find the prime factors of 109 and 224:
Prime factors of 109 = 109
Prime factors of 224 = 2 x 2 x 2 x 2 x 2 x 7
step 3Identify the repeated and non-repeated prime factors of 109 and 224:
Since there is no common factors between 109 and 224, multiplying the given numbers directly provides the LCM of
109 and 224.
= 109 x 224
= 24416
lcm(109 and 224) = 24416
Hence,
lcm of 109 and 224 is 24416
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 109 and 224.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 109 and 224
What to be found:
lcm (109, 224) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
109 and 224
step 3 Choose the divisor which divides each or most of the given integers (109 and 224), 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 224 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 109 | 224 |
| 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 224:
= 2 x 2 x 2 x 2 x 2 x 7 x 109
= 24416
LCM(109, 224) = 24416
The LCM of two numbers 109 and 224 is 24416