LCM of 129 and 312
13416 is the LCM of 129 and 312. 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 129 and 312, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 129 and 312?
lcm (129 312) = (?)
129 => 3 x 43
312 => 2 x 2 x 2 x 3 x 13
= 3 x 43 x 2 x 2 x 2 x 13
= 13416
lcm (129 and 312) = 13416
13416 is the LCM of 129 and 312.
where,
129 is a positive integer,
312 is a positive integer,
13416 is the LCM of 129 and 312,
{3} in {3 x 43, 2 x 2 x 2 x 3 x 13} is the common factors of 129 and 312,
{43 x 2 x 2 x 2 x 13} in {3 x 43, 2 x 2 x 2 x 3 x 13} are the uncommon factors of 129 and 312.
Use in Mathematics: LCM of 129 and 312
The below are some of the mathematical applications where lcm of 129 and 312 can be used:
- to find the least number which is exactly divisible by 129 and 312.
- to find the common denominator for two fractions having 129 and 312 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 129 and 312 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 129 seconds and bell B tolls at 312 seconds repeatedly. The answer is that all bells A and B toll together at 13416 seconds for the first time, at 26832 seconds for the second time, at 40248 seconds for the third time and so on.
Important Notes: 129 and 312 lcm
The below are the important notes to be remembered while solving the lcm of 129 and 312:
- The common prime factors and the remaining prime factors of 129 and 312 should be multiplied to find the least common multiple of 129 and 312, when solving lcm by using prime factors method.
- The results of lcm of 129 and 312, and the lcm of 312 and 129 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 129 and 312?
The below solved example with step by step work shows how to find what is the lcm of 129 and 312 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 129 and 312?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 129
B = 312
What to be found:
find the lcm of 129 and 312
step 2 Find the prime factors of 129 and 312:
Prime factors of 129 = 3 x 43
Prime factors of 312 = 2 x 2 x 2 x 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 129 and 312:
{3} is the most repeated factor and {43 x 2 x 2 x 2 x 13} are the non-repeated factors of 129 and 312.
step 4 Find the product of repeated and non-repeated prime factors of 129 and 312:
= 3 x 43 x 2 x 2 x 2 x 13
= 13416
lcm(129 and 312) = 13416
Hence,
lcm of 129 and 312 is 13416
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 129 and 312.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 129 and 312
What to be found:
lcm (129, 312) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
129 and 312
step 3 Choose the divisor which divides each or most of the given integers (129 and 312), 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 129 and 312 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 129 | 312 |
| 2 | 129 | 156 |
| 2 | 129 | 78 |
| 3 | 129 | 39 |
| 13 | 43 | 13 |
| 43 | 43 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 129 and 312:
= 2 x 2 x 2 x 3 x 13 x 43
= 13416
LCM(129, 312) = 13416
The LCM of two numbers 129 and 312 is 13416