# 12 and 15 LCM LCM of 12 and 15 is equal to 60. The comprehensive work provides more insight of how to find what is the lcm of 12 and 15 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

what is the lcm of 12 and 15?
lcm (12   15) = (?)
12 => 2 x 2 x 3
15 => 3 x 5

= 3 x 2 x 2 x 5
= 60
lcm (12 and 15) = 60
60 is the lcm of 12 and 15.

where,
12 is a positive integer,
15 is a positive integer,
60 is the lcm of 12 and 15,
{3} in {2 x 2 x 3, 3 x 5} is the common factors of 12 and 15,
{2 x 2 x 5} in {2 x 2 x 3, 3 x 5} are the uncommon factors of 12 and 15.

Use in Mathematics: LCM of 12 and 15
The below are some of the mathematical applications where lcm of 12 and 15 can be used:

1. to find the least number which is exactly divisible by 12 and 15.
2. to find the common denominator for two fractions having 12 and 15 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 12 and 15 lcm
In the context of lcm real world problems, the lcm of 12 and 15 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 12 seconds and bell B tolls at 15 seconds repeatedly. The answer is that all bells A and B toll together at 60 seconds for the first time, at 120 seconds for the second time, at 180 seconds for the third time and so on.

Important Notes: 12 and 15 lcm
The below are the important notes to be remembered while solving the lcm of 12 and 15:
1. The common prime factors and the remaining prime factors of 12 and 15 should be multiplied to find the least common multiple of 12 and 15, when solving lcm by using prime factors method.
2. The results of lcm of 12 and 15, and the lcm of 15 and 12 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
For values other than 12 and 15, use this below tool:

## How-to: What is the LCM of 12 and 15?

The below solved example with step by step work shows how to find what is the lcm of 12 and 15 by using prime factors method and division method.

Solved example using prime factors method:
What is the LCM of 12 and 15?

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 12
B = 15

What to be found:
find the lcm of 12 and 15

step 2 Find the prime factors of 12 and 15:
Prime factors of 12 = 2 x 2 x 3
Prime factors of 15 = 3 x 5

step 3 Identify the repeated and non-repeated prime factors of 12 and 15:
{3} is the most repeated factor and {2 x 2 x 5} are the non-repeated factors of 12 and 15.

step 4 Find the product of repeated and non-repeated prime factors of 12 and 15:
= 3 x 2 x 2 x 5
= 60
lcm(12 and 15) = 60

Hence,
lcm of 12 and 15 is 60

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 12 and 15.

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 12 and 15

What to be found:
lcm (12, 15) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:
12 and 15

step 3 Choose the divisor which divides each or most of the given integers (12 and 15), 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 12 and 15 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

 2 12 15 2 6 15 3 3 15 5 1 5 1 1

step 4 Multiply the divisors to find the lcm of 12 and 15:
= 2 x 2 x 3 x 5
= 60
LCM(12, 15) = 60

The least common multiple for two numbers 12 and 15 is 60 