LCM of 123 and 297
12177 is the LCM of 123 and 297. 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 297, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 123 and 297?
lcm (123 297) = (?)
123 => 3 x 41
297 => 3 x 3 x 3 x 11
= 3 x 41 x 3 x 3 x 11
= 12177
lcm (123 and 297) = 12177
12177 is the LCM of 123 and 297.
where,
123 is a positive integer,
297 is a positive integer,
12177 is the LCM of 123 and 297,
{3} in {3 x 41, 3 x 3 x 3 x 11} is the common factors of 123 and 297,
{41 x 3 x 3 x 11} in {3 x 41, 3 x 3 x 3 x 11} are the uncommon factors of 123 and 297.
Use in Mathematics: LCM of 123 and 297
The below are some of the mathematical applications where lcm of 123 and 297 can be used:
- to find the least number which is exactly divisible by 123 and 297.
- to find the common denominator for two fractions having 123 and 297 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 123 and 297 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 297 seconds repeatedly. The answer is that all bells A and B toll together at 12177 seconds for the first time, at 24354 seconds for the second time, at 36531 seconds for the third time and so on.
Important Notes: 123 and 297 lcm
The below are the important notes to be remembered while solving the lcm of 123 and 297:
- The common prime factors and the remaining prime factors of 123 and 297 should be multiplied to find the least common multiple of 123 and 297, when solving lcm by using prime factors method.
- The results of lcm of 123 and 297, and the lcm of 297 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 297?
The below solved example with step by step work shows how to find what is the lcm of 123 and 297 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 123 and 297?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 123
B = 297
What to be found:
find the lcm of 123 and 297
step 2 Find the prime factors of 123 and 297:
Prime factors of 123 = 3 x 41
Prime factors of 297 = 3 x 3 x 3 x 11
step 3 Identify the repeated and non-repeated prime factors of 123 and 297:
{3} is the most repeated factor and {41 x 3 x 3 x 11} are the non-repeated factors of 123 and 297.
step 4 Find the product of repeated and non-repeated prime factors of 123 and 297:
= 3 x 41 x 3 x 3 x 11
= 12177
lcm(123 and 297) = 12177
Hence,
lcm of 123 and 297 is 12177
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 123 and 297.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 123 and 297
What to be found:
lcm (123, 297) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
123 and 297
step 3 Choose the divisor which divides each or most of the given integers (123 and 297), 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 297 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 123 | 297 |
| 3 | 41 | 99 |
| 3 | 41 | 33 |
| 11 | 41 | 11 |
| 41 | 41 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 123 and 297:
= 3 x 3 x 3 x 11 x 41
= 12177
LCM(123, 297) = 12177
The LCM of two numbers 123 and 297 is 12177