LCM of 321 and 340
109140 is the LCM of 321 and 340. 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 340, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 321 and 340?
lcm (321 340) = (?)
321 => 3 x 107
340 => 2 x 2 x 5 x 17
= 3 x 107 x 2 x 2 x 5 x 17
= 109140
lcm (321 and 340) = 109140
109140 is the LCM of 321 and 340.
where,
321 is a positive integer,
340 is a positive integer,
109140 is the LCM of 321 and 340,
There is no common factors of 321 and 340 in {3 x 107, 2 x 2 x 5 x 17},
{3 x 107 x 2 x 2 x 5 x 17} in {3 x 107, 2 x 2 x 5 x 17} are the uncommon factors of 321 and 340.
Use in Mathematics: LCM of 321 and 340
The below are some of the mathematical applications where lcm of 321 and 340 can be used:
- to find the least number which is exactly divisible by 321 and 340.
- to find the common denominator for two fractions having 321 and 340 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 321 and 340 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 340 seconds repeatedly. The answer is that all bells A and B toll together at 109140 seconds for the first time, at 218280 seconds for the second time, at 327420 seconds for the third time and so on.
Important Notes: 321 and 340 lcm
The below are the important notes to be remembered while solving the lcm of 321 and 340:
- The common prime factors and the remaining prime factors of 321 and 340 should be multiplied to find the least common multiple of 321 and 340, when solving lcm by using prime factors method.
- The results of lcm of 321 and 340, and the lcm of 340 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 340?
The below solved example with step by step work shows how to find what is the lcm of 321 and 340 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 321 and 340?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 321
B = 340
What to be found:
find the lcm of 321 and 340
step 2 Find the prime factors of 321 and 340:
Prime factors of 321 = 3 x 107
Prime factors of 340 = 2 x 2 x 5 x 17
step 3Identify the repeated and non-repeated prime factors of 321 and 340:
Since there is no common factors between 321 and 340, multiplying the given numbers directly provides the LCM of
321 and 340.
= 321 x 340
= 109140
lcm(321 and 340) = 109140
Hence,
lcm of 321 and 340 is 109140
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 321 and 340.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 321 and 340
What to be found:
lcm (321, 340) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
321 and 340
step 3 Choose the divisor which divides each or most of the given integers (321 and 340), 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 340 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 321 | 340 |
| 2 | 321 | 170 |
| 3 | 321 | 85 |
| 5 | 107 | 85 |
| 17 | 107 | 17 |
| 107 | 107 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 321 and 340:
= 2 x 2 x 3 x 5 x 17 x 107
= 109140
LCM(321, 340) = 109140
The LCM of two numbers 321 and 340 is 109140