LCM of 129 and 213
9159 is the LCM of 129 and 213. 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 213, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 129 and 213?
lcm (129 213) = (?)
129 => 3 x 43
213 => 3 x 71
= 3 x 43 x 71
= 9159
lcm (129 and 213) = 9159
9159 is the LCM of 129 and 213.
where,
129 is a positive integer,
213 is a positive integer,
9159 is the LCM of 129 and 213,
{3} in {3 x 43, 3 x 71} is the common factors of 129 and 213,
{43 x 71} in {3 x 43, 3 x 71} are the uncommon factors of 129 and 213.
Use in Mathematics: LCM of 129 and 213
The below are some of the mathematical applications where lcm of 129 and 213 can be used:
- to find the least number which is exactly divisible by 129 and 213.
- to find the common denominator for two fractions having 129 and 213 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 129 and 213 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 213 seconds repeatedly. The answer is that all bells A and B toll together at 9159 seconds for the first time, at 18318 seconds for the second time, at 27477 seconds for the third time and so on.
Important Notes: 129 and 213 lcm
The below are the important notes to be remembered while solving the lcm of 129 and 213:
- The common prime factors and the remaining prime factors of 129 and 213 should be multiplied to find the least common multiple of 129 and 213, when solving lcm by using prime factors method.
- The results of lcm of 129 and 213, and the lcm of 213 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 213?
The below solved example with step by step work shows how to find what is the lcm of 129 and 213 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 129 and 213?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 129
B = 213
What to be found:
find the lcm of 129 and 213
step 2 Find the prime factors of 129 and 213:
Prime factors of 129 = 3 x 43
Prime factors of 213 = 3 x 71
step 3 Identify the repeated and non-repeated prime factors of 129 and 213:
{3} is the most repeated factor and {43 x 71} are the non-repeated factors of 129 and 213.
step 4 Find the product of repeated and non-repeated prime factors of 129 and 213:
= 3 x 43 x 71
= 9159
lcm(129 and 213) = 9159
Hence,
lcm of 129 and 213 is 9159
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 129 and 213.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 129 and 213
What to be found:
lcm (129, 213) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
129 and 213
step 3 Choose the divisor which divides each or most of the given integers (129 and 213), 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 213 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 129 | 213 |
| 43 | 43 | 71 |
| 71 | 1 | 71 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 129 and 213:
= 3 x 43 x 71
= 9159
LCM(129, 213) = 9159
The LCM of two numbers 129 and 213 is 9159