LCM of 189 and 309
19467 is the LCM of 189 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 189 and 309, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 189 and 309?
lcm (189 309) = (?)
189 => 3 x 3 x 3 x 7
309 => 3 x 103
= 3 x 3 x 3 x 7 x 103
= 19467
lcm (189 and 309) = 19467
19467 is the LCM of 189 and 309.
where,
189 is a positive integer,
309 is a positive integer,
19467 is the LCM of 189 and 309,
{3} in {3 x 3 x 3 x 7, 3 x 103} is the common factors of 189 and 309,
{3 x 3 x 7 x 103} in {3 x 3 x 3 x 7, 3 x 103} are the uncommon factors of 189 and 309.
Use in Mathematics: LCM of 189 and 309
The below are some of the mathematical applications where lcm of 189 and 309 can be used:
- to find the least number which is exactly divisible by 189 and 309.
- to find the common denominator for two fractions having 189 and 309 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 189 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 189 seconds and bell B tolls at 309 seconds repeatedly. The answer is that all bells A and B toll together at 19467 seconds for the first time, at 38934 seconds for the second time, at 58401 seconds for the third time and so on.
Important Notes: 189 and 309 lcm
The below are the important notes to be remembered while solving the lcm of 189 and 309:
- The common prime factors and the remaining prime factors of 189 and 309 should be multiplied to find the least common multiple of 189 and 309, when solving lcm by using prime factors method.
- The results of lcm of 189 and 309, and the lcm of 309 and 189 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 189 and 309?
The below solved example with step by step work shows how to find what is the lcm of 189 and 309 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 189 and 309?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 189
B = 309
What to be found:
find the lcm of 189 and 309
step 2 Find the prime factors of 189 and 309:
Prime factors of 189 = 3 x 3 x 3 x 7
Prime factors of 309 = 3 x 103
step 3 Identify the repeated and non-repeated prime factors of 189 and 309:
{3} is the most repeated factor and {3 x 3 x 7 x 103} are the non-repeated factors of 189 and 309.
step 4 Find the product of repeated and non-repeated prime factors of 189 and 309:
= 3 x 3 x 3 x 7 x 103
= 19467
lcm(189 and 309) = 19467
Hence,
lcm of 189 and 309 is 19467
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 189 and 309.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 189 and 309
What to be found:
lcm (189, 309) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
189 and 309
step 3 Choose the divisor which divides each or most of the given integers (189 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 189 and 309 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 189 | 309 |
| 3 | 63 | 103 |
| 3 | 21 | 103 |
| 7 | 7 | 103 |
| 103 | 1 | 103 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 189 and 309:
= 3 x 3 x 3 x 7 x 103
= 19467
LCM(189, 309) = 19467
The LCM of two numbers 189 and 309 is 19467