LCM of 312 and 355
110760 is the LCM of 312 and 355. 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 355, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 312 and 355?
lcm (312 355) = (?)
312 => 2 x 2 x 2 x 3 x 13
355 => 5 x 71
= 2 x 2 x 2 x 3 x 13 x 5 x 71
= 110760
lcm (312 and 355) = 110760
110760 is the LCM of 312 and 355.
where,
312 is a positive integer,
355 is a positive integer,
110760 is the LCM of 312 and 355,
There is no common factors of 312 and 355 in {2 x 2 x 2 x 3 x 13, 5 x 71},
{2 x 2 x 2 x 3 x 13 x 5 x 71} in {2 x 2 x 2 x 3 x 13, 5 x 71} are the uncommon factors of 312 and 355.
Use in Mathematics: LCM of 312 and 355
The below are some of the mathematical applications where lcm of 312 and 355 can be used:
- to find the least number which is exactly divisible by 312 and 355.
- to find the common denominator for two fractions having 312 and 355 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 312 and 355 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 355 seconds repeatedly. The answer is that all bells A and B toll together at 110760 seconds for the first time, at 221520 seconds for the second time, at 332280 seconds for the third time and so on.
Important Notes: 312 and 355 lcm
The below are the important notes to be remembered while solving the lcm of 312 and 355:
- The common prime factors and the remaining prime factors of 312 and 355 should be multiplied to find the least common multiple of 312 and 355, when solving lcm by using prime factors method.
- The results of lcm of 312 and 355, and the lcm of 355 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 355?
The below solved example with step by step work shows how to find what is the lcm of 312 and 355 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 312 and 355?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 312
B = 355
What to be found:
find the lcm of 312 and 355
step 2 Find the prime factors of 312 and 355:
Prime factors of 312 = 2 x 2 x 2 x 3 x 13
Prime factors of 355 = 5 x 71
step 3Identify the repeated and non-repeated prime factors of 312 and 355:
Since there is no common factors between 312 and 355, multiplying the given numbers directly provides the LCM of
312 and 355.
= 312 x 355
= 110760
lcm(312 and 355) = 110760
Hence,
lcm of 312 and 355 is 110760
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 312 and 355.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 312 and 355
What to be found:
lcm (312, 355) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
312 and 355
step 3 Choose the divisor which divides each or most of the given integers (312 and 355), 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 355 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 312 | 355 |
| 2 | 156 | 355 |
| 2 | 78 | 355 |
| 3 | 39 | 355 |
| 5 | 13 | 355 |
| 13 | 13 | 71 |
| 71 | 1 | 71 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 312 and 355:
= 2 x 2 x 2 x 3 x 5 x 13 x 71
= 110760
LCM(312, 355) = 110760
The LCM of two numbers 312 and 355 is 110760