LCM of 129 and 162
6966 is the LCM of 129 and 162. 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 162, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 129 and 162?
lcm (129 162) = (?)
129 => 3 x 43
162 => 2 x 3 x 3 x 3 x 3
= 3 x 43 x 2 x 3 x 3 x 3
= 6966
lcm (129 and 162) = 6966
6966 is the LCM of 129 and 162.
where,
129 is a positive integer,
162 is a positive integer,
6966 is the LCM of 129 and 162,
{3} in {3 x 43, 2 x 3 x 3 x 3 x 3} is the common factors of 129 and 162,
{43 x 2 x 3 x 3 x 3} in {3 x 43, 2 x 3 x 3 x 3 x 3} are the uncommon factors of 129 and 162.
Use in Mathematics: LCM of 129 and 162
The below are some of the mathematical applications where lcm of 129 and 162 can be used:
- to find the least number which is exactly divisible by 129 and 162.
- to find the common denominator for two fractions having 129 and 162 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 129 and 162 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 162 seconds repeatedly. The answer is that all bells A and B toll together at 6966 seconds for the first time, at 13932 seconds for the second time, at 20898 seconds for the third time and so on.
Important Notes: 129 and 162 lcm
The below are the important notes to be remembered while solving the lcm of 129 and 162:
- The common prime factors and the remaining prime factors of 129 and 162 should be multiplied to find the least common multiple of 129 and 162, when solving lcm by using prime factors method.
- The results of lcm of 129 and 162, and the lcm of 162 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 162?
The below solved example with step by step work shows how to find what is the lcm of 129 and 162 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 129 and 162?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 129
B = 162
What to be found:
find the lcm of 129 and 162
step 2 Find the prime factors of 129 and 162:
Prime factors of 129 = 3 x 43
Prime factors of 162 = 2 x 3 x 3 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 129 and 162:
{3} is the most repeated factor and {43 x 2 x 3 x 3 x 3} are the non-repeated factors of 129 and 162.
step 4 Find the product of repeated and non-repeated prime factors of 129 and 162:
= 3 x 43 x 2 x 3 x 3 x 3
= 6966
lcm(129 and 162) = 6966
Hence,
lcm of 129 and 162 is 6966
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 129 and 162.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 129 and 162
What to be found:
lcm (129, 162) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
129 and 162
step 3 Choose the divisor which divides each or most of the given integers (129 and 162), 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 162 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 129 | 162 |
| 3 | 129 | 81 |
| 3 | 43 | 27 |
| 3 | 43 | 9 |
| 3 | 43 | 3 |
| 43 | 43 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 129 and 162:
= 2 x 3 x 3 x 3 x 3 x 43
= 6966
LCM(129, 162) = 6966
The LCM of two numbers 129 and 162 is 6966