LCM of 123 and 308
37884 is the LCM of 123 and 308. 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 308, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 123 and 308?
lcm (123 308) = (?)
123 => 3 x 41
308 => 2 x 2 x 7 x 11
= 3 x 41 x 2 x 2 x 7 x 11
= 37884
lcm (123 and 308) = 37884
37884 is the LCM of 123 and 308.
where,
123 is a positive integer,
308 is a positive integer,
37884 is the LCM of 123 and 308,
There is no common factors of 123 and 308 in {3 x 41, 2 x 2 x 7 x 11},
{3 x 41 x 2 x 2 x 7 x 11} in {3 x 41, 2 x 2 x 7 x 11} are the uncommon factors of 123 and 308.
Use in Mathematics: LCM of 123 and 308
The below are some of the mathematical applications where lcm of 123 and 308 can be used:
- to find the least number which is exactly divisible by 123 and 308.
- to find the common denominator for two fractions having 123 and 308 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 123 and 308 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 308 seconds repeatedly. The answer is that all bells A and B toll together at 37884 seconds for the first time, at 75768 seconds for the second time, at 113652 seconds for the third time and so on.
Important Notes: 123 and 308 lcm
The below are the important notes to be remembered while solving the lcm of 123 and 308:
- The common prime factors and the remaining prime factors of 123 and 308 should be multiplied to find the least common multiple of 123 and 308, when solving lcm by using prime factors method.
- The results of lcm of 123 and 308, and the lcm of 308 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 308?
The below solved example with step by step work shows how to find what is the lcm of 123 and 308 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 123 and 308?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 123
B = 308
What to be found:
find the lcm of 123 and 308
step 2 Find the prime factors of 123 and 308:
Prime factors of 123 = 3 x 41
Prime factors of 308 = 2 x 2 x 7 x 11
step 3Identify the repeated and non-repeated prime factors of 123 and 308:
Since there is no common factors between 123 and 308, multiplying the given numbers directly provides the LCM of
123 and 308.
= 123 x 308
= 37884
lcm(123 and 308) = 37884
Hence,
lcm of 123 and 308 is 37884
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 123 and 308.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 123 and 308
What to be found:
lcm (123, 308) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
123 and 308
step 3 Choose the divisor which divides each or most of the given integers (123 and 308), 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 308 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 123 | 308 |
| 2 | 123 | 154 |
| 3 | 123 | 77 |
| 7 | 41 | 77 |
| 11 | 41 | 11 |
| 41 | 41 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 123 and 308:
= 2 x 2 x 3 x 7 x 11 x 41
= 37884
LCM(123, 308) = 37884
The LCM of two numbers 123 and 308 is 37884