LCM of 312 and 325
7800 is the LCM of 312 and 325. 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 312 and 325, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 312 and 325?
lcm (312 325) = (?)
312 => 2 x 2 x 2 x 3 x 13
325 => 5 x 5 x 13
= 13 x 2 x 2 x 2 x 3 x 5 x 5
= 7800
lcm (312 and 325) = 7800
7800 is the LCM of 312 and 325.
where,
312 is a positive integer,
325 is a positive integer,
7800 is the LCM of 312 and 325,
{13} in {2 x 2 x 2 x 3 x 13, 5 x 5 x 13} is the common factors of 312 and 325,
{2 x 2 x 2 x 3 x 5 x 5} in {2 x 2 x 2 x 3 x 13, 5 x 5 x 13} are the uncommon factors of 312 and 325.
Use in Mathematics: LCM of 312 and 325
The below are some of the mathematical applications where lcm of 312 and 325 can be used:
- to find the least number which is exactly divisible by 312 and 325.
- to find the common denominator for two fractions having 312 and 325 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 312 and 325 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 312 seconds and bell B tolls at 325 seconds repeatedly. The answer is that all bells A and B toll together at 7800 seconds for the first time, at 15600 seconds for the second time, at 23400 seconds for the third time and so on.
Important Notes: 312 and 325 lcm
The below are the important notes to be remembered while solving the lcm of 312 and 325:
- The common prime factors and the remaining prime factors of 312 and 325 should be multiplied to find the least common multiple of 312 and 325, when solving lcm by using prime factors method.
- The results of lcm of 312 and 325, and the lcm of 325 and 312 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 312 and 325?
The below solved example with step by step work shows how to find what is the lcm of 312 and 325 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 312 and 325?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 312
B = 325
What to be found:
find the lcm of 312 and 325
step 2 Find the prime factors of 312 and 325:
Prime factors of 312 = 2 x 2 x 2 x 3 x 13
Prime factors of 325 = 5 x 5 x 13
step 3 Identify the repeated and non-repeated prime factors of 312 and 325:
{13} is the most repeated factor and {2 x 2 x 2 x 3 x 5 x 5} are the non-repeated factors of 312 and 325.
step 4 Find the product of repeated and non-repeated prime factors of 312 and 325:
= 13 x 2 x 2 x 2 x 3 x 5 x 5
= 7800
lcm(312 and 325) = 7800
Hence,
lcm of 312 and 325 is 7800
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 312 and 325.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 312 and 325
What to be found:
lcm (312, 325) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
312 and 325
step 3 Choose the divisor which divides each or most of the given integers (312 and 325), 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 312 and 325 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 312 | 325 |
| 2 | 156 | 325 |
| 2 | 78 | 325 |
| 3 | 39 | 325 |
| 5 | 13 | 325 |
| 5 | 13 | 65 |
| 13 | 13 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 312 and 325:
= 2 x 2 x 2 x 3 x 5 x 5 x 13
= 7800
LCM(312, 325) = 7800
The LCM of two numbers 312 and 325 is 7800