LCM of 168 and 309
17304 is the LCM of 168 and 309. 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 168 and 309, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 168 and 309?
lcm (168 309) = (?)
168 => 2 x 2 x 2 x 3 x 7
309 => 3 x 103
= 3 x 2 x 2 x 2 x 7 x 103
= 17304
lcm (168 and 309) = 17304
17304 is the LCM of 168 and 309.
where,
168 is a positive integer,
309 is a positive integer,
17304 is the LCM of 168 and 309,
{3} in {2 x 2 x 2 x 3 x 7, 3 x 103} is the common factors of 168 and 309,
{2 x 2 x 2 x 7 x 103} in {2 x 2 x 2 x 3 x 7, 3 x 103} are the uncommon factors of 168 and 309.
Use in Mathematics: LCM of 168 and 309
The below are some of the mathematical applications where lcm of 168 and 309 can be used:
- to find the least number which is exactly divisible by 168 and 309.
- to find the common denominator for two fractions having 168 and 309 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 168 and 309 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 168 seconds and bell B tolls at 309 seconds repeatedly. The answer is that all bells A and B toll together at 17304 seconds for the first time, at 34608 seconds for the second time, at 51912 seconds for the third time and so on.
Important Notes: 168 and 309 lcm
The below are the important notes to be remembered while solving the lcm of 168 and 309:
- The common prime factors and the remaining prime factors of 168 and 309 should be multiplied to find the least common multiple of 168 and 309, when solving lcm by using prime factors method.
- The results of lcm of 168 and 309, and the lcm of 309 and 168 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 168 and 309?
The below solved example with step by step work shows how to find what is the lcm of 168 and 309 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 168 and 309?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 168
B = 309
What to be found:
find the lcm of 168 and 309
step 2 Find the prime factors of 168 and 309:
Prime factors of 168 = 2 x 2 x 2 x 3 x 7
Prime factors of 309 = 3 x 103
step 3 Identify the repeated and non-repeated prime factors of 168 and 309:
{3} is the most repeated factor and {2 x 2 x 2 x 7 x 103} are the non-repeated factors of 168 and 309.
step 4 Find the product of repeated and non-repeated prime factors of 168 and 309:
= 3 x 2 x 2 x 2 x 7 x 103
= 17304
lcm(168 and 309) = 17304
Hence,
lcm of 168 and 309 is 17304
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 168 and 309.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 168 and 309
What to be found:
lcm (168, 309) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
168 and 309
step 3 Choose the divisor which divides each or most of the given integers (168 and 309), 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 168 and 309 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 168 | 309 |
| 2 | 84 | 309 |
| 2 | 42 | 309 |
| 3 | 21 | 309 |
| 7 | 7 | 103 |
| 103 | 1 | 103 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 168 and 309:
= 2 x 2 x 2 x 3 x 7 x 103
= 17304
LCM(168, 309) = 17304
The LCM of two numbers 168 and 309 is 17304