LCM of 12 and 24
24 is the LCM of 12 and 24. 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 12 and 24, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 12 and 24?
lcm (12 24) = (?)
12 => 2 x 2 x 3
24 => 2 x 2 x 2 x 3
= 2 x 2 x 3 x 2
= 24
lcm (12 and 24) = 24
24 is the LCM of 12 and 24.
where,
12 is a positive integer,
24 is a positive integer,
24 is the LCM of 12 and 24,
{2 x 2 x 3} in {2 x 2 x 3, 2 x 2 x 2 x 3} are the common factors of 12 and 24,
{2} in {2 x 2 x 3, 2 x 2 x 2 x 3} is the uncommon factors of 12 and 24.
Use in Mathematics: LCM of 12 and 24
The below are some of the mathematical applications where lcm of 12 and 24 can be used:
- to find the least number which is exactly divisible by 12 and 24.
- to find the common denominator for two fractions having 12 and 24 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 12 and 24 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 24 seconds repeatedly. The answer is that all bells A and B toll together at 24 seconds for the first time, at 48 seconds for the second time, at 72 seconds for the third time and so on.
Important Notes: 12 and 24 lcm
The below are the important notes to be remembered while solving the lcm of 12 and 24:
- The common prime factors and the remaining prime factors of 12 and 24 should be multiplied to find the least common multiple of 12 and 24, when solving lcm by using prime factors method.
- The results of lcm of 12 and 24, and the lcm of 24 and 12 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 12 and 24?
The below solved example with step by step work shows how to find what is the lcm of 12 and 24 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 12 and 24?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 12
B = 24
What to be found:
find the lcm of 12 and 24
step 2 Find the prime factors of 12 and 24:
Prime factors of 12 = 2 x 2 x 3
Prime factors of 24 = 2 x 2 x 2 x 3
step 3 Identify the repeated and non-repeated prime factors of 12 and 24:
{2, 2, 3} are the most repeated factors and {2} is the non-repeated factor of 12 and 24.
step 4 Find the product of repeated and non-repeated prime factors of 12 and 24:
= 2 x 2 x 3 x 2
= 24
lcm(12 and 24) = 24
Hence,
lcm of 12 and 24 is 24
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 12 and 24.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 12 and 24
What to be found:
lcm (12, 24) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
12 and 24
step 3 Choose the divisor which divides each or most of the given integers (12 and 24), 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 24 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 12 | 24 |
| 2 | 6 | 12 |
| 2 | 3 | 6 |
| 3 | 3 | 3 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 12 and 24:
= 2 x 2 x 2 x 3
= 24
LCM(12, 24) = 24
The LCM of two numbers 12 and 24 is 24