LCM of 312 and 354
18408 is the LCM of 312 and 354. 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 354, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 312 and 354?
lcm (312 354) = (?)
312 => 2 x 2 x 2 x 3 x 13
354 => 2 x 3 x 59
= 2 x 3 x 2 x 2 x 13 x 59
= 18408
lcm (312 and 354) = 18408
18408 is the LCM of 312 and 354.
where,
312 is a positive integer,
354 is a positive integer,
18408 is the LCM of 312 and 354,
{2 x 3} in {2 x 2 x 2 x 3 x 13, 2 x 3 x 59} are the common factors of 312 and 354,
{2 x 2 x 13 x 59} in {2 x 2 x 2 x 3 x 13, 2 x 3 x 59} are the uncommon factors of 312 and 354.
Use in Mathematics: LCM of 312 and 354
The below are some of the mathematical applications where lcm of 312 and 354 can be used:
- to find the least number which is exactly divisible by 312 and 354.
- to find the common denominator for two fractions having 312 and 354 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 312 and 354 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 354 seconds repeatedly. The answer is that all bells A and B toll together at 18408 seconds for the first time, at 36816 seconds for the second time, at 55224 seconds for the third time and so on.
Important Notes: 312 and 354 lcm
The below are the important notes to be remembered while solving the lcm of 312 and 354:
- The common prime factors and the remaining prime factors of 312 and 354 should be multiplied to find the least common multiple of 312 and 354, when solving lcm by using prime factors method.
- The results of lcm of 312 and 354, and the lcm of 354 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 354?
The below solved example with step by step work shows how to find what is the lcm of 312 and 354 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 312 and 354?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 312
B = 354
What to be found:
find the lcm of 312 and 354
step 2 Find the prime factors of 312 and 354:
Prime factors of 312 = 2 x 2 x 2 x 3 x 13
Prime factors of 354 = 2 x 3 x 59
step 3 Identify the repeated and non-repeated prime factors of 312 and 354:
{2, 3} are the most repeated factors and {2 x 2 x 13 x 59} are the non-repeated factors of 312 and 354.
step 4 Find the product of repeated and non-repeated prime factors of 312 and 354:
= 2 x 3 x 2 x 2 x 13 x 59
= 18408
lcm(312 and 354) = 18408
Hence,
lcm of 312 and 354 is 18408
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 312 and 354.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 312 and 354
What to be found:
lcm (312, 354) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
312 and 354
step 3 Choose the divisor which divides each or most of the given integers (312 and 354), 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 354 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 312 | 354 |
| 2 | 156 | 177 |
| 2 | 78 | 177 |
| 3 | 39 | 177 |
| 13 | 13 | 59 |
| 59 | 1 | 59 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 312 and 354:
= 2 x 2 x 2 x 3 x 13 x 59
= 18408
LCM(312, 354) = 18408
The LCM of two numbers 312 and 354 is 18408