# 30 and 80 LCM LCM of 30 and 80 is equal to 240. The comprehensive work provides more insight of how to find what is the lcm of 30 and 80 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

what is the lcm of 30 and 80?
lcm (30   80) = (?)
30 => 2 x 3 x 5
80 => 2 x 2 x 2 x 2 x 5

= 2 x 5 x 3 x 2 x 2 x 2
= 240
lcm (30 and 80) = 240
240 is the lcm of 30 and 80.

where,
30 is a positive integer,
80 is a positive integer,
240 is the lcm of 30 and 80,
{2 x 5} in {2 x 3 x 5, 2 x 2 x 2 x 2 x 5} are the common factors of 30 and 80,
{3 x 2 x 2 x 2} in {2 x 3 x 5, 2 x 2 x 2 x 2 x 5} are the uncommon factors of 30 and 80.

Use in Mathematics: LCM of 30 and 80
The below are some of the mathematical applications where lcm of 30 and 80 can be used:

1. to find the least number which is exactly divisible by 30 and 80.
2. to find the common denominator for two fractions having 30 and 80 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 30 and 80 lcm
In the context of lcm real world problems, the lcm of 30 and 80 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 30 seconds and bell B tolls at 80 seconds repeatedly. The answer is that all bells A and B toll together at 240 seconds for the first time, at 480 seconds for the second time, at 720 seconds for the third time and so on.

Important Notes: 30 and 80 lcm
The below are the important notes to be remembered while solving the lcm of 30 and 80:
1. The common prime factors and the remaining prime factors of 30 and 80 should be multiplied to find the least common multiple of 30 and 80, when solving lcm by using prime factors method.
2. The results of lcm of 30 and 80, and the lcm of 80 and 30 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
For values other than 30 and 80, use this below tool:

## How-to: What is the LCM of 30 and 80?

The below solved example with step by step work shows how to find what is the lcm of 30 and 80 by using prime factors method and division method.

Solved example using prime factors method:
What is the LCM of 30 and 80?

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 30
B = 80

What to be found:
find the lcm of 30 and 80

step 2 Find the prime factors of 30 and 80:
Prime factors of 30 = 2 x 3 x 5
Prime factors of 80 = 2 x 2 x 2 x 2 x 5

step 3 Identify the repeated and non-repeated prime factors of 30 and 80:
{2, 5} are the most repeated factors and {3 x 2 x 2 x 2} are the non-repeated factors of 30 and 80.

step 4 Find the product of repeated and non-repeated prime factors of 30 and 80:
= 2 x 5 x 3 x 2 x 2 x 2
= 240
lcm(30 and 80) = 240

Hence,
lcm of 30 and 80 is 240

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 30 and 80.

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 30 and 80

What to be found:
lcm (30, 80) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:
30 and 80

step 3 Choose the divisor which divides each or most of the given integers (30 and 80), 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 30 and 80 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

 2 30 80 2 15 40 2 15 20 2 15 10 3 15 5 5 5 5 1 1

step 4 Multiply the divisors to find the lcm of 30 and 80:
= 2 x 2 x 2 x 2 x 3 x 5
= 240
LCM(30, 80) = 240

The least common multiple for two numbers 30 and 80 is 240 