LCM of 321 and 326
104646 is the LCM of 321 and 326. 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 321 and 326, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 321 and 326?
lcm (321 326) = (?)
321 => 3 x 107
326 => 2 x 163
= 3 x 107 x 2 x 163
= 104646
lcm (321 and 326) = 104646
104646 is the LCM of 321 and 326.
where,
321 is a positive integer,
326 is a positive integer,
104646 is the LCM of 321 and 326,
There is no common factors of 321 and 326 in {3 x 107, 2 x 163},
{3 x 107 x 2 x 163} in {3 x 107, 2 x 163} are the uncommon factors of 321 and 326.
Use in Mathematics: LCM of 321 and 326
The below are some of the mathematical applications where lcm of 321 and 326 can be used:
- to find the least number which is exactly divisible by 321 and 326.
- to find the common denominator for two fractions having 321 and 326 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 321 and 326 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 321 seconds and bell B tolls at 326 seconds repeatedly. The answer is that all bells A and B toll together at 104646 seconds for the first time, at 209292 seconds for the second time, at 313938 seconds for the third time and so on.
Important Notes: 321 and 326 lcm
The below are the important notes to be remembered while solving the lcm of 321 and 326:
- The common prime factors and the remaining prime factors of 321 and 326 should be multiplied to find the least common multiple of 321 and 326, when solving lcm by using prime factors method.
- The results of lcm of 321 and 326, and the lcm of 326 and 321 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 321 and 326?
The below solved example with step by step work shows how to find what is the lcm of 321 and 326 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 321 and 326?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 321
B = 326
What to be found:
find the lcm of 321 and 326
step 2 Find the prime factors of 321 and 326:
Prime factors of 321 = 3 x 107
Prime factors of 326 = 2 x 163
step 3Identify the repeated and non-repeated prime factors of 321 and 326:
Since there is no common factors between 321 and 326, multiplying the given numbers directly provides the LCM of
321 and 326.
= 321 x 326
= 104646
lcm(321 and 326) = 104646
Hence,
lcm of 321 and 326 is 104646
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 321 and 326.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 321 and 326
What to be found:
lcm (321, 326) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
321 and 326
step 3 Choose the divisor which divides each or most of the given integers (321 and 326), 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 321 and 326 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 321 | 326 |
| 3 | 321 | 163 |
| 107 | 107 | 163 |
| 163 | 1 | 163 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 321 and 326:
= 2 x 3 x 107 x 163
= 104646
LCM(321, 326) = 104646
The LCM of two numbers 321 and 326 is 104646