LCM of 164 and 312
12792 is the LCM of 164 and 312. 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 164 and 312, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 164 and 312?
lcm (164 312) = (?)
164 => 2 x 2 x 41
312 => 2 x 2 x 2 x 3 x 13
= 2 x 2 x 41 x 2 x 3 x 13
= 12792
lcm (164 and 312) = 12792
12792 is the LCM of 164 and 312.
where,
164 is a positive integer,
312 is a positive integer,
12792 is the LCM of 164 and 312,
{2 x 2} in {2 x 2 x 41, 2 x 2 x 2 x 3 x 13} are the common factors of 164 and 312,
{41 x 2 x 3 x 13} in {2 x 2 x 41, 2 x 2 x 2 x 3 x 13} are the uncommon factors of 164 and 312.
Use in Mathematics: LCM of 164 and 312
The below are some of the mathematical applications where lcm of 164 and 312 can be used:
- to find the least number which is exactly divisible by 164 and 312.
- to find the common denominator for two fractions having 164 and 312 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 164 and 312 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 164 seconds and bell B tolls at 312 seconds repeatedly. The answer is that all bells A and B toll together at 12792 seconds for the first time, at 25584 seconds for the second time, at 38376 seconds for the third time and so on.
Important Notes: 164 and 312 lcm
The below are the important notes to be remembered while solving the lcm of 164 and 312:
- The common prime factors and the remaining prime factors of 164 and 312 should be multiplied to find the least common multiple of 164 and 312, when solving lcm by using prime factors method.
- The results of lcm of 164 and 312, and the lcm of 312 and 164 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 164 and 312?
The below solved example with step by step work shows how to find what is the lcm of 164 and 312 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 164 and 312?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 164
B = 312
What to be found:
find the lcm of 164 and 312
step 2 Find the prime factors of 164 and 312:
Prime factors of 164 = 2 x 2 x 41
Prime factors of 312 = 2 x 2 x 2 x 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 164 and 312:
{2, 2} are the most repeated factors and {41 x 2 x 3 x 13} are the non-repeated factors of 164 and 312.
step 4 Find the product of repeated and non-repeated prime factors of 164 and 312:
= 2 x 2 x 41 x 2 x 3 x 13
= 12792
lcm(164 and 312) = 12792
Hence,
lcm of 164 and 312 is 12792
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 164 and 312.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 164 and 312
What to be found:
lcm (164, 312) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
164 and 312
step 3 Choose the divisor which divides each or most of the given integers (164 and 312), 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 164 and 312 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 164 | 312 |
| 2 | 82 | 156 |
| 2 | 41 | 78 |
| 3 | 41 | 39 |
| 13 | 41 | 13 |
| 41 | 41 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 164 and 312:
= 2 x 2 x 2 x 3 x 13 x 41
= 12792
LCM(164, 312) = 12792
The LCM of two numbers 164 and 312 is 12792