# 108 and 180 LCM LCM of 108 and 180 is equal to 540. The comprehensive work provides more insight of how to find what is the lcm of 108 and 180 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

what is the lcm of 108 and 180?
lcm (108   180) = (?)
108 => 2 x 2 x 3 x 3 x 3
180 => 2 x 2 x 3 x 3 x 5

= 2 x 2 x 3 x 3 x 3 x 5
= 540
lcm (108 and 180) = 540
540 is the lcm of 108 and 180.

where,
108 is a positive integer,
180 is a positive integer,
540 is the lcm of 108 and 180,
{2 x 2 x 3 x 3} in {2 x 2 x 3 x 3 x 3, 2 x 2 x 3 x 3 x 5} are the common factors of 108 and 180,
{3 x 5} in {2 x 2 x 3 x 3 x 3, 2 x 2 x 3 x 3 x 5} are the uncommon factors of 108 and 180.

Use in Mathematics: LCM of 108 and 180
The below are some of the mathematical applications where lcm of 108 and 180 can be used:

1. to find the least number which is exactly divisible by 108 and 180.
2. to find the common denominator for two fractions having 108 and 180 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 108 and 180 lcm
In the context of lcm real world problems, the lcm of 108 and 180 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 108 seconds and bell B tolls at 180 seconds repeatedly. The answer is that all bells A and B toll together at 540 seconds for the first time, at 1080 seconds for the second time, at 1620 seconds for the third time and so on.

Important Notes: 108 and 180 lcm
The below are the important notes to be remembered while solving the lcm of 108 and 180:
1. The common prime factors and the remaining prime factors of 108 and 180 should be multiplied to find the least common multiple of 108 and 180, when solving lcm by using prime factors method.
2. The results of lcm of 108 and 180, and the lcm of 180 and 108 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
For values other than 108 and 180, use this below tool:

## How-to: What is the LCM of 108 and 180?

The below solved example with step by step work shows how to find what is the lcm of 108 and 180 by using prime factors method and division method.

Solved example using prime factors method:
What is the LCM of 108 and 180?

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 108
B = 180

What to be found:
find the lcm of 108 and 180

step 2 Find the prime factors of 108 and 180:
Prime factors of 108 = 2 x 2 x 3 x 3 x 3
Prime factors of 180 = 2 x 2 x 3 x 3 x 5

step 3 Identify the repeated and non-repeated prime factors of 108 and 180:
{2, 2, 3, 3} are the most repeated factors and {3 x 5} are the non-repeated factors of 108 and 180.

step 4 Find the product of repeated and non-repeated prime factors of 108 and 180:
= 2 x 2 x 3 x 3 x 3 x 5
= 540
lcm(108 and 180) = 540

Hence,
lcm of 108 and 180 is 540

Solved example using special division method:
This special division method is the easiest way to understand the entire calculation of what is the lcm of 108 and 180.

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 108 and 180

What to be found:
lcm (108, 180) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:
108 and 180

step 3 Choose the divisor which divides each or most of the given integers (108 and 180), 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 108 and 180 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

 2 108 180 2 54 90 3 27 45 3 9 15 3 3 5 5 1 5 1 1

step 4 Multiply the divisors to find the lcm of 108 and 180:
= 2 x 2 x 3 x 3 x 3 x 5
= 540
LCM(108, 180) = 540

The least common multiple for two numbers 108 and 180 is 540 