LCM of 123 and 357
14637 is the LCM of 123 and 357. 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 357, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 123 and 357?
lcm (123 357) = (?)
123 => 3 x 41
357 => 3 x 7 x 17
= 3 x 41 x 7 x 17
= 14637
lcm (123 and 357) = 14637
14637 is the LCM of 123 and 357.
where,
123 is a positive integer,
357 is a positive integer,
14637 is the LCM of 123 and 357,
{3} in {3 x 41, 3 x 7 x 17} is the common factors of 123 and 357,
{41 x 7 x 17} in {3 x 41, 3 x 7 x 17} are the uncommon factors of 123 and 357.
Use in Mathematics: LCM of 123 and 357
The below are some of the mathematical applications where lcm of 123 and 357 can be used:
- to find the least number which is exactly divisible by 123 and 357.
- to find the common denominator for two fractions having 123 and 357 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 123 and 357 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 357 seconds repeatedly. The answer is that all bells A and B toll together at 14637 seconds for the first time, at 29274 seconds for the second time, at 43911 seconds for the third time and so on.
Important Notes: 123 and 357 lcm
The below are the important notes to be remembered while solving the lcm of 123 and 357:
- The common prime factors and the remaining prime factors of 123 and 357 should be multiplied to find the least common multiple of 123 and 357, when solving lcm by using prime factors method.
- The results of lcm of 123 and 357, and the lcm of 357 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 357?
The below solved example with step by step work shows how to find what is the lcm of 123 and 357 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 123 and 357?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 123
B = 357
What to be found:
find the lcm of 123 and 357
step 2 Find the prime factors of 123 and 357:
Prime factors of 123 = 3 x 41
Prime factors of 357 = 3 x 7 x 17
step 3 Identify the repeated and non-repeated prime factors of 123 and 357:
{3} is the most repeated factor and {41 x 7 x 17} are the non-repeated factors of 123 and 357.
step 4 Find the product of repeated and non-repeated prime factors of 123 and 357:
= 3 x 41 x 7 x 17
= 14637
lcm(123 and 357) = 14637
Hence,
lcm of 123 and 357 is 14637
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 123 and 357.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 123 and 357
What to be found:
lcm (123, 357) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
123 and 357
step 3 Choose the divisor which divides each or most of the given integers (123 and 357), 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 357 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 123 | 357 |
| 7 | 41 | 119 |
| 17 | 41 | 17 |
| 41 | 41 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 123 and 357:
= 3 x 7 x 17 x 41
= 14637
LCM(123, 357) = 14637
The LCM of two numbers 123 and 357 is 14637