LCM of 123 and 344
42312 is the LCM of 123 and 344. 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 123 and 344, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 123 and 344?
lcm (123 344) = (?)
123 => 3 x 41
344 => 2 x 2 x 2 x 43
= 3 x 41 x 2 x 2 x 2 x 43
= 42312
lcm (123 and 344) = 42312
42312 is the LCM of 123 and 344.
where,
123 is a positive integer,
344 is a positive integer,
42312 is the LCM of 123 and 344,
There is no common factors of 123 and 344 in {3 x 41, 2 x 2 x 2 x 43},
{3 x 41 x 2 x 2 x 2 x 43} in {3 x 41, 2 x 2 x 2 x 43} are the uncommon factors of 123 and 344.
Use in Mathematics: LCM of 123 and 344
The below are some of the mathematical applications where lcm of 123 and 344 can be used:
- to find the least number which is exactly divisible by 123 and 344.
- to find the common denominator for two fractions having 123 and 344 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 123 and 344 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 123 seconds and bell B tolls at 344 seconds repeatedly. The answer is that all bells A and B toll together at 42312 seconds for the first time, at 84624 seconds for the second time, at 126936 seconds for the third time and so on.
Important Notes: 123 and 344 lcm
The below are the important notes to be remembered while solving the lcm of 123 and 344:
- The common prime factors and the remaining prime factors of 123 and 344 should be multiplied to find the least common multiple of 123 and 344, when solving lcm by using prime factors method.
- The results of lcm of 123 and 344, and the lcm of 344 and 123 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 123 and 344?
The below solved example with step by step work shows how to find what is the lcm of 123 and 344 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 123 and 344?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 123
B = 344
What to be found:
find the lcm of 123 and 344
step 2 Find the prime factors of 123 and 344:
Prime factors of 123 = 3 x 41
Prime factors of 344 = 2 x 2 x 2 x 43
step 3Identify the repeated and non-repeated prime factors of 123 and 344:
Since there is no common factors between 123 and 344, multiplying the given numbers directly provides the LCM of
123 and 344.
= 123 x 344
= 42312
lcm(123 and 344) = 42312
Hence,
lcm of 123 and 344 is 42312
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 123 and 344.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 123 and 344
What to be found:
lcm (123, 344) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
123 and 344
step 3 Choose the divisor which divides each or most of the given integers (123 and 344), 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 123 and 344 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 123 | 344 |
| 2 | 123 | 172 |
| 2 | 123 | 86 |
| 3 | 123 | 43 |
| 41 | 41 | 43 |
| 43 | 1 | 43 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 123 and 344:
= 2 x 2 x 2 x 3 x 41 x 43
= 42312
LCM(123, 344) = 42312
The LCM of two numbers 123 and 344 is 42312