LCM of 12 and 87
348 is the LCM of 12 and 87. 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 87, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 12 and 87?
lcm (12 87) = (?)
12 => 2 x 2 x 3
87 => 3 x 29
= 3 x 2 x 2 x 29
= 348
lcm (12 and 87) = 348
348 is the LCM of 12 and 87.
where,
12 is a positive integer,
87 is a positive integer,
348 is the LCM of 12 and 87,
{3} in {2 x 2 x 3, 3 x 29} is the common factors of 12 and 87,
{2 x 2 x 29} in {2 x 2 x 3, 3 x 29} are the uncommon factors of 12 and 87.
Use in Mathematics: LCM of 12 and 87
The below are some of the mathematical applications where lcm of 12 and 87 can be used:
- to find the least number which is exactly divisible by 12 and 87.
- to find the common denominator for two fractions having 12 and 87 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 12 and 87 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 87 seconds repeatedly. The answer is that all bells A and B toll together at 348 seconds for the first time, at 696 seconds for the second time, at 1044 seconds for the third time and so on.
Important Notes: 12 and 87 lcm
The below are the important notes to be remembered while solving the lcm of 12 and 87:
- The common prime factors and the remaining prime factors of 12 and 87 should be multiplied to find the least common multiple of 12 and 87, when solving lcm by using prime factors method.
- The results of lcm of 12 and 87, and the lcm of 87 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 87?
The below solved example with step by step work shows how to find what is the lcm of 12 and 87 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 12 and 87?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 12
B = 87
What to be found:
find the lcm of 12 and 87
step 2 Find the prime factors of 12 and 87:
Prime factors of 12 = 2 x 2 x 3
Prime factors of 87 = 3 x 29
step 3 Identify the repeated and non-repeated prime factors of 12 and 87:
{3} is the most repeated factor and {2 x 2 x 29} are the non-repeated factors of 12 and 87.
step 4 Find the product of repeated and non-repeated prime factors of 12 and 87:
= 3 x 2 x 2 x 29
= 348
lcm(12 and 87) = 348
Hence,
lcm of 12 and 87 is 348
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 12 and 87.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 12 and 87
What to be found:
lcm (12, 87) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
12 and 87
step 3 Choose the divisor which divides each or most of the given integers (12 and 87), 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 87 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 12 | 87 |
| 2 | 6 | 87 |
| 3 | 3 | 87 |
| 29 | 1 | 29 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 12 and 87:
= 2 x 2 x 3 x 29
= 348
LCM(12, 87) = 348
The LCM of two numbers 12 and 87 is 348