LCM of 12 and 39
156 is the LCM of 12 and 39. 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 39, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 12 and 39?
lcm (12 39) = (?)
12 => 2 x 2 x 3
39 => 3 x 13
= 3 x 2 x 2 x 13
= 156
lcm (12 and 39) = 156
156 is the LCM of 12 and 39.
where,
12 is a positive integer,
39 is a positive integer,
156 is the LCM of 12 and 39,
{3} in {2 x 2 x 3, 3 x 13} is the common factors of 12 and 39,
{2 x 2 x 13} in {2 x 2 x 3, 3 x 13} are the uncommon factors of 12 and 39.
Use in Mathematics: LCM of 12 and 39
The below are some of the mathematical applications where lcm of 12 and 39 can be used:
- to find the least number which is exactly divisible by 12 and 39.
- to find the common denominator for two fractions having 12 and 39 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 12 and 39 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 39 seconds repeatedly. The answer is that all bells A and B toll together at 156 seconds for the first time, at 312 seconds for the second time, at 468 seconds for the third time and so on.
Important Notes: 12 and 39 lcm
The below are the important notes to be remembered while solving the lcm of 12 and 39:
- The common prime factors and the remaining prime factors of 12 and 39 should be multiplied to find the least common multiple of 12 and 39, when solving lcm by using prime factors method.
- The results of lcm of 12 and 39, and the lcm of 39 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 39?
The below solved example with step by step work shows how to find what is the lcm of 12 and 39 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 12 and 39?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 12
B = 39
What to be found:
find the lcm of 12 and 39
step 2 Find the prime factors of 12 and 39:
Prime factors of 12 = 2 x 2 x 3
Prime factors of 39 = 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 12 and 39:
{3} is the most repeated factor and {2 x 2 x 13} are the non-repeated factors of 12 and 39.
step 4 Find the product of repeated and non-repeated prime factors of 12 and 39:
= 3 x 2 x 2 x 13
= 156
lcm(12 and 39) = 156
Hence,
lcm of 12 and 39 is 156
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 12 and 39.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 12 and 39
What to be found:
lcm (12, 39) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
12 and 39
step 3 Choose the divisor which divides each or most of the given integers (12 and 39), 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 39 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 12 | 39 |
| 2 | 6 | 39 |
| 3 | 3 | 39 |
| 13 | 1 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 12 and 39:
= 2 x 2 x 3 x 13
= 156
LCM(12, 39) = 156
The LCM of two numbers 12 and 39 is 156