36 and 108 LCM
LCM of 36 and 108 is equal to 108. The comprehensive work provides more insight of how to find what is the lcm of 36 and 108 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 36 and 108?
lcm (36 108) = (?)
36 => 2 x 2 x 3 x 3
108 => 2 x 2 x 3 x 3 x 3
= 2 x 2 x 3 x 3 x 3
= 108
lcm (36 and 108) = 108
108 is the lcm of 36 and 108.
where,
36 is a positive integer,
108 is a positive integer,
108 is the lcm of 36 and 108,
{2 x 2 x 3 x 3} in {2 x 2 x 3 x 3, 2 x 2 x 3 x 3 x 3} are the common factors of 36 and 108,
{3} in {2 x 2 x 3 x 3, 2 x 2 x 3 x 3 x 3} is the uncommon factors of 36 and 108.
Use in Mathematics: LCM of 36 and 108
The below are some of the mathematical applications where lcm of 36 and 108 can be used:
- to find the least number which is exactly divisible by 36 and 108.
- to find the common denominator for two fractions having 36 and 108 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 36 and 108 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 36 seconds and bell B tolls at 108 seconds repeatedly. The answer is that all bells A and B toll together at 108 seconds for the first time, at 216 seconds for the second time, at 324 seconds for the third time and so on.
Important Notes: 36 and 108 lcm
The below are the important notes to be remembered while solving the lcm of 36 and 108:
- The common prime factors and the remaining prime factors of 36 and 108 should be multiplied to find the least common multiple of 36 and 108, when solving lcm by using prime factors method.
- The results of lcm of 36 and 108, and the lcm of 108 and 36 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 36 and 108?
The below solved example with step by step work shows how to find what is the lcm of 36 and 108 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 36 and 108?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 36
B = 108
What to be found:
find the lcm of 36 and 108
step 2 Find the prime factors of 36 and 108:
Prime factors of 36 = 2 x 2 x 3 x 3
Prime factors of 108 = 2 x 2 x 3 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 36 and 108:
{2, 2, 3, 3} are the most repeated factors and {3} is the non-repeated factor of 36 and 108.
step 4 Find the product of repeated and non-repeated prime factors of 36 and 108:
= 2 x 2 x 3 x 3 x 3
= 108
lcm(36 and 108) = 108
Hence,
lcm of 36 and 108 is 108
This special division method is the easiest way to understand the entire calculation of what is the lcm of 36 and 108.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 36 and 108
What to be found:
lcm (36, 108) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
36 and 108
step 3 Choose the divisor which divides each or most of the given integers (36 and 108), 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 36 and 108 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 36 | 108 |
| 2 | 18 | 54 |
| 3 | 9 | 27 |
| 3 | 3 | 9 |
| 3 | 1 | 3 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 36 and 108:
= 2 x 2 x 3 x 3 x 3
= 108
LCM(36, 108) = 108
The least common multiple for two numbers 36 and 108 is 108