LCM of 136 and 324
11016 is the LCM of 136 and 324. 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 136 and 324, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 136 and 324?
lcm (136 324) = (?)
136 => 2 x 2 x 2 x 17
324 => 2 x 2 x 3 x 3 x 3 x 3
= 2 x 2 x 2 x 17 x 3 x 3 x 3 x 3
= 11016
lcm (136 and 324) = 11016
11016 is the LCM of 136 and 324.
where,
136 is a positive integer,
324 is a positive integer,
11016 is the LCM of 136 and 324,
{2 x 2} in {2 x 2 x 2 x 17, 2 x 2 x 3 x 3 x 3 x 3} are the common factors of 136 and 324,
{2 x 17 x 3 x 3 x 3 x 3} in {2 x 2 x 2 x 17, 2 x 2 x 3 x 3 x 3 x 3} are the uncommon factors of 136 and 324.
Use in Mathematics: LCM of 136 and 324
The below are some of the mathematical applications where lcm of 136 and 324 can be used:
- to find the least number which is exactly divisible by 136 and 324.
- to find the common denominator for two fractions having 136 and 324 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 136 and 324 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 136 seconds and bell B tolls at 324 seconds repeatedly. The answer is that all bells A and B toll together at 11016 seconds for the first time, at 22032 seconds for the second time, at 33048 seconds for the third time and so on.
Important Notes: 136 and 324 lcm
The below are the important notes to be remembered while solving the lcm of 136 and 324:
- The common prime factors and the remaining prime factors of 136 and 324 should be multiplied to find the least common multiple of 136 and 324, when solving lcm by using prime factors method.
- The results of lcm of 136 and 324, and the lcm of 324 and 136 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 136 and 324?
The below solved example with step by step work shows how to find what is the lcm of 136 and 324 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 136 and 324?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 136
B = 324
What to be found:
find the lcm of 136 and 324
step 2 Find the prime factors of 136 and 324:
Prime factors of 136 = 2 x 2 x 2 x 17
Prime factors of 324 = 2 x 2 x 3 x 3 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 136 and 324:
{2, 2} are the most repeated factors and {2 x 17 x 3 x 3 x 3 x 3} are the non-repeated factors of 136 and 324.
step 4 Find the product of repeated and non-repeated prime factors of 136 and 324:
= 2 x 2 x 2 x 17 x 3 x 3 x 3 x 3
= 11016
lcm(136 and 324) = 11016
Hence,
lcm of 136 and 324 is 11016
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 136 and 324.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 136 and 324
What to be found:
lcm (136, 324) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
136 and 324
step 3 Choose the divisor which divides each or most of the given integers (136 and 324), 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 136 and 324 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 136 | 324 |
| 2 | 68 | 162 |
| 2 | 34 | 81 |
| 3 | 17 | 81 |
| 3 | 17 | 27 |
| 3 | 17 | 9 |
| 3 | 17 | 3 |
| 17 | 17 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 136 and 324:
= 2 x 2 x 2 x 3 x 3 x 3 x 3 x 17
= 11016
LCM(136, 324) = 11016
The LCM of two numbers 136 and 324 is 11016