LCM of 209 and 247
2717 is the LCM of 209 and 247. 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 209 and 247, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 209 and 247?
lcm (209 247) = (?)
209 => 11 x 19
247 => 13 x 19
= 19 x 11 x 13
= 2717
lcm (209 and 247) = 2717
2717 is the LCM of 209 and 247.
where,
209 is a positive integer,
247 is a positive integer,
2717 is the LCM of 209 and 247,
{19} in {11 x 19, 13 x 19} is the common factors of 209 and 247,
{11 x 13} in {11 x 19, 13 x 19} are the uncommon factors of 209 and 247.
Use in Mathematics: LCM of 209 and 247
The below are some of the mathematical applications where lcm of 209 and 247 can be used:
- to find the least number which is exactly divisible by 209 and 247.
- to find the common denominator for two fractions having 209 and 247 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 209 and 247 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 209 seconds and bell B tolls at 247 seconds repeatedly. The answer is that all bells A and B toll together at 2717 seconds for the first time, at 5434 seconds for the second time, at 8151 seconds for the third time and so on.
Important Notes: 209 and 247 lcm
The below are the important notes to be remembered while solving the lcm of 209 and 247:
- The common prime factors and the remaining prime factors of 209 and 247 should be multiplied to find the least common multiple of 209 and 247, when solving lcm by using prime factors method.
- The results of lcm of 209 and 247, and the lcm of 247 and 209 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 209 and 247?
The below solved example with step by step work shows how to find what is the lcm of 209 and 247 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 209 and 247?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 209
B = 247
What to be found:
find the lcm of 209 and 247
step 2 Find the prime factors of 209 and 247:
Prime factors of 209 = 11 x 19
Prime factors of 247 = 13 x 19
step 3 Identify the repeated and non-repeated prime factors of 209 and 247:
{19} is the most repeated factor and {11 x 13} are the non-repeated factors of 209 and 247.
step 4 Find the product of repeated and non-repeated prime factors of 209 and 247:
= 19 x 11 x 13
= 2717
lcm(209 and 247) = 2717
Hence,
lcm of 209 and 247 is 2717
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 209 and 247.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 209 and 247
What to be found:
lcm (209, 247) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
209 and 247
step 3 Choose the divisor which divides each or most of the given integers (209 and 247), 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 209 and 247 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 11 | 209 | 247 |
| 13 | 19 | 247 |
| 19 | 19 | 19 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 209 and 247:
= 11 x 13 x 19
= 2717
LCM(209, 247) = 2717
The LCM of two numbers 209 and 247 is 2717