LCM of 309 and 340
105060 is the LCM of 309 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 309 and 340, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 309 and 340?
lcm (309 340) = (?)
309 => 3 x 103
340 => 2 x 2 x 5 x 17
= 3 x 103 x 2 x 2 x 5 x 17
= 105060
lcm (309 and 340) = 105060
105060 is the LCM of 309 and 340.
where,
309 is a positive integer,
340 is a positive integer,
105060 is the LCM of 309 and 340,
There is no common factors of 309 and 340 in {3 x 103, 2 x 2 x 5 x 17},
{3 x 103 x 2 x 2 x 5 x 17} in {3 x 103, 2 x 2 x 5 x 17} are the uncommon factors of 309 and 340.
Use in Mathematics: LCM of 309 and 340
The below are some of the mathematical applications where lcm of 309 and 340 can be used:
- to find the least number which is exactly divisible by 309 and 340.
- to find the common denominator for two fractions having 309 and 340 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 309 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 309 seconds and bell B tolls at 340 seconds repeatedly. The answer is that all bells A and B toll together at 105060 seconds for the first time, at 210120 seconds for the second time, at 315180 seconds for the third time and so on.
Important Notes: 309 and 340 lcm
The below are the important notes to be remembered while solving the lcm of 309 and 340:
- The common prime factors and the remaining prime factors of 309 and 340 should be multiplied to find the least common multiple of 309 and 340, when solving lcm by using prime factors method.
- The results of lcm of 309 and 340, and the lcm of 340 and 309 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 309 and 340?
The below solved example with step by step work shows how to find what is the lcm of 309 and 340 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 309 and 340?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 309
B = 340
What to be found:
find the lcm of 309 and 340
step 2 Find the prime factors of 309 and 340:
Prime factors of 309 = 3 x 103
Prime factors of 340 = 2 x 2 x 5 x 17
step 3Identify the repeated and non-repeated prime factors of 309 and 340:
Since there is no common factors between 309 and 340, multiplying the given numbers directly provides the LCM of
309 and 340.
= 309 x 340
= 105060
lcm(309 and 340) = 105060
Hence,
lcm of 309 and 340 is 105060
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 309 and 340.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 309 and 340
What to be found:
lcm (309, 340) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
309 and 340
step 3 Choose the divisor which divides each or most of the given integers (309 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 309 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 | 309 | 340 |
| 2 | 309 | 170 |
| 3 | 309 | 85 |
| 5 | 103 | 85 |
| 17 | 103 | 17 |
| 103 | 103 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 309 and 340:
= 2 x 2 x 3 x 5 x 17 x 103
= 105060
LCM(309, 340) = 105060
The LCM of two numbers 309 and 340 is 105060